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One thing that other answers don't seem to have covered is that you only need a very thin layer of electrical insulator (at modest voltages) while the heat spreader part of a heat sink works best if it's thick. So it's more efficient to use a thin electrically-insulating barrier followed by a thick, cheap, and easily-made metal heatsink than it would be to use a single piece of a material that's thermally conductive and electrically insulating. The few materials that do exist (such as diamond) can't be extruded or otherwise easily formed into a heatsink shape. Some can be sintered but sintering can't generally reach the thermal conductivity of bulk material. The engineering effect of all this materials science is that we end up doing what we've always done.

Another factor is stock policies: by stocking bulky robust heatsinks and a smaller number (as they're not always required) of small delicate insulating pads your stock occupies less storage space and capital than if you stocked two types of bulky heatsink. Cost and performance are both better without the insulator when it's not required.

This is hardly a new problem; those of us of a certain age remember the heatsinks with mica insulators for the TO-220 and TO-3 packages.

The issue (at the time) was both material cost and availability and materials science. We have come a long way in our understanding of thermal conductivity of various compounds over the years, but it is still relatively new technology (there are things such as thermally conductive pads that have been around for decades but are not really heat sinks in their own right).

The TO-220 has the heat spreader on the collector / drain of the device, which is usually at an elevated voltage, so the typical arrangement used this technique:

Source.

It was not unusual to use some thermal paste as well to maximise the heat transfer.

Now that does not really explain the relative rarity of integrated insulated heatsinks; that really comes down to 'is it necessary' or can I simply use the well known method of a heat sink and an electrically insulating barrier material which is less expensive (at least, it is today).

The old tried and true method has served well for many decades, but for some applications (particularly those in small devices) such a solution may well not fit.

There are quite a few offerings available, but they tend to be a bit more expensive (on a per watt basis). There is also a lot of research into other materials.

Of course, for the bling factor, you could use these.

So it comes down to a number of things and cost is a major driver. I will also note that a large market for heat sinks is for CPUs and GPUs where the case of the IC is electrically insulated anyway.

Polymer heatsinks deserve a mention. Polymer heatsinks aren't that uncommon. I come across polymer heat sinks industrial, automotive, prosumer goods once in a while. They are often hard to recognize as heatsinks, because they can have a second mechanical purposes (an enclosure, a bracket, a reflector of a lamp). These heat sinks are always custom injection-molded parts.

Polymers have a small heat conductivity, compared to any metal. This prompts a question: how can a polymer make an acceptable heatsink? In some cases, the thermal resistance of the heatsink becomes dominated by transfer from heatsink to air, rather than by conduction within the heatsink itself. This can happen when dumping heat into air with natural convection. In these cases, a heatsink made of a special polymer with a relatively high thermal conduction ( $ mathrm20 frac W mcdot K $ ) can be comparable to an aluminium ( $ mathrm200 frac W mcdot K $ ) heatsink with the same geometry.

E2 is the plastic (source)

Some additional discussion in this old answer.

The thing about a heat sink is that there are only really two ways to ultimately dispose of the heat, conduction and radiation.

So ultimately, assuming your emmisivity is reasonably close to 1 (Only really matters if you can run HOT, power loss to radiation is 4th power of absolute temperature), and you can make the thing have good thermal contact with the surrounding cooling media (Air, water, whatever), what you make it from only matters a little (That interface is the killer for performance, not the bulk thermal conductivity of the heatsink).

Now clearly you need to design the heatsink so that heat travels thru it reasonably efficiently and in the area where there is a lot of power flux density that might argue for something other then ally, for the bulk of the thing where you have plenty of metal to keep delta T low, cheapest is best.

For a heat spreader or insulating washer it is different of course, heat spreaders by definition are used where the power flux density is very high and minimal thermal resistance is a very good thing, hence the usual use of copper in this role.

For the insulator you do see exotic materials used, because a good thermal conductor that is also an electrical insulator is not that common, so Boron Nitride, Alumina, Beryllium Oxide(!) and the like all see service here, and I would not be shocked by someone using diamond (Probably in some weird RF device).

From a technical standpoint its certainly possible to manufacture heatsinks with built in isolator pads. The reason they don't do it is economics.

Between the different mechanical, electrical, and thermal choices there are a lot of different combinations. If the isolator and heatsink were one part then the vendors would have to stock a lot more unique part numbers.

By factoring out the isolator and heat sink into unique products the user has a lot more choices.

Here are some of the things to consider.

1) In many cases the user will use gap pads between heat-sinks and hot components to pick up slack in mechanical tolerances. This means that each user will want the pad to be a different thickness.

2) Thermal isolator pad materials vary in how well they are able to conform to rough surfaces. There is often a trade between how squishy the material is and how well it conducts heat.

3) Different users will have different isolation requirements in terms of voltage. There is a trade off between isolation voltage, the material thickness and the thermal resistance.

3) Adding an insulator between a heat-sink and a part has a penalty in terms of thermal resistance. If its possible to not use an insulating layer then you will get the best thermal performance in that case.

The best compromise is to make an extremely thin large surface area layer with a high rated Voltage [kV/mm] with sufficient hardness to not be cut or punctured but must also be low cost.

Thermally conductive insulator characteristics include;

Cost-effective
Resistant to tears and cut-through
High dielectric strength
UL94 VO rated options available
Low ageing rate: Pads do not dry out, ooze out or crack 
Gap Filling, if burrs, roughness or planarity is a problem
Compatibility (gas sensors must be non-silicone and LED interfaces must be non-organic)
Low dielectric constant for capacitance load on collector/drain tabs on high dV/dt high voltage drivers

All electrical insulators are "dielectrics".
All heatsinks are good thermal conductors.

Yet in solids, it can be expensive to have both as good characteristics.
Phase change materials that turn fluid under pressure to make a possible solution.

CPU's tend to use ceramic-glass as the thermal top to the heatsink due to extremely flat properties.

For line voltage Triacs, Mica was the best material for 5kV pulse protection and thermal conduction with thermal grease.

Dielectrics fluids like transformer oil also good thermal insulators with the flow of heat.

Figures of merit for comparing materials Thermally conductive Insulators use;

Thermal Conductivity [W/m-K],

thickness [um], shore hardness [00],

Dielectric Strength [kV/mm] and

Thermal Impedance [˚C-cm²/W]

$fracVmm cdot frac°Ccdot mmW$ or divide by thermal conduction in $frackVmm /fracWm-K$.

Traditional solutions; have been Mica, 3M tape and some polymers tapes.

Aavid Thermalloy's best economical solution is :

Thermalsil III

 uses finely woven glass cloth with a silicone elastomer binder 0.152mm thick
 Dielectric Strength : 26 kV/mm 
 Thermal Conductivity: 0.92 W/m'C 
 UL 94V-0

For forced-air heat removal, it is not the CFM that counts, but is often reported, rather it is the turbulent surface air velocity that controls cooling in mean [m/s].

The product of both these parameters leads to the best material properties but not the cheapest.

Actually, there is a good solution: Aluminum. Anodized aluminum. The anodization turns the surface into Aluminum Oxide, which is an insulator. Good News: The surface area is increased to help conduct the heat to the ambient air; Bad News not a flat, smooth surface to contact the power device making the heat. Solution: Thermal Compound (aka "Grease"). Important notes: there are several processes to anodize aluminum. Most of the pretty stuff is "Class I" which is soft or "Class II" which is moderately hard. You can use Class II If there is no relative movement of the device to be cooled and it is solidly clamped to the heat sink and there are no burrs or scratches, this works well. Too many "if"s & "and"s for you? Then "Class III" anodization is what you want. It tends to be unevenly colored and the black has a brownish or purplish hue. It is almost as hard as diamonds, and pretty much scratch proof. Still needs Grease, but no insulator at reasonable voltages. The military & aerospace have used this for over 50 years, either as thin (~ 0.025") anodized washers (similar to die punched mica TO-3 insulators) or the entire enclosure (think missiles). Hard to find now-a-days and costs more than other solutions, but does the job well.

For the "grease", use silicone (not petroleum based), Aluminum Oxide (not Zinc Oxide) from Dow, Shin-Etsu, Fuji-Poly, or Saint-Gobain. The boutique silver and copper based stuff for overclocking PCs 'gamers' use is both expensive and conductive. This is OK with Class III anodization, as long as it doesn't migrate, fall, dry out, powder or flake, etc. onto the current carrying stuff (just don't use it). If you really need to couple a lot of heat with grease, Beryllium Oxide is several times better than Aluminum Oxide. Just treat it like asbestos: don't lick it, don't eat it, don't breath it in. It is a skin irritant, so wear gloves, and prepare for the onslaught of a "toxic witch hunt". These greases only need to be 0.0001" to 0.0005" thick under the device (kind of translucent). Apply with a small plastic or metal squeegee; for production volumes use a stencil (same type of stencil material as used for solder paste ~0.005" SS) and a squeegee.

I have seen heat-sinks with a thin ceramic coating in the mounting area, but the difference of Cte is an issue and can crack the thin ceramic.

Hope this helps, I got this from >40 years of wandering between electrons and electron holes.

Overall I suspect that avoiding "wear" in the field and consequent expensive replacement is a key reason for general applications avoiding crystalline heatsinks. Not saying that metal heatsinks never fail in the field. But generally speaking replacement of metal heatsinks in the field would be a lot cheaper and require a lot less specialized equipment compared to crystalline heatsinks.

That is at the start crystalline heatsinks would be generally expensive to machine to shape and some out right breakage would occur due thermal and mechanical stress. You might still stay within acceptable total costs if all that happened at special heatsink factory. But its not uncommon for end application manufacturers to need to trim heatsink to fit etc.

Second once in a fielded application, many heatsinks experience thermal and mechanical shock and vibration which might be outside the 100% survival rate for crystalline heatsinks. Good old metal heatsinks on the other hand can take quite a bit of abuse and flexing. Some even serve secondarily as a mechanical fastening point to the outer chassis of a larger assembly.

Also in the case of crystalline heatsinks the fasteners might become points of failure instead of the heatsink. A softer fastener would damp out vibration damage to the heatsink but instead be gradually sawed through by those same vibrations and flexing.

So crystalline heatsinks would probably become an occasional repair item in the field...assuming smart thermal shutdown and alerts. Now think what special tools are needed in the field and what sort of breakage rates might apply when your average tech tries to deal with replacement. I bet heatsinks would be something many corps, governments, and private customers would expect local techs to handle even if not circuits. Just a wrench job right?