A series of wells a few micrometers wide in a silicon substrate, doped to make use of the thermoelectric effect, ought to be able to do temperature cycling at kilohertz, by 50+ degrees C.
It's the kind of thing that could be built in a university silicon lab too.
If you're using off the shelf plastics as your reaction vessel (which most of these do), then you're immediately stuck with these large thermal mass systems.
A few reasons why many of these machines stay away from microfluidics:
PCR reactions are notoriously susceptible to cross-contamination, so microfluidics wells would either need to be thoroughly cleaned (a pain), or just single use (this is what we do with most plastics... - which would be expensive).
How do you get your stuff into the well! Current scale plastics had amendable to human operators (infinitely flexible, minimal capital cost, easy to replace). The equipment you need (basically a good pipette and tips) is relatively cheap and well understood. To do this at the microfluidics scale would be much more expensive (and see the same cleaning concern from above).
What are you doing with your PCR result? Assuming that you're just going with florescent probes, having the giant macro-scale lump of liquid gives you both a physically very large target, and a relatively brighter target to look for. This can certainly be overcome, but is more engineering work.
If you were using PCR as an upstream process (dunno how common this is now anymore), then you need to generate enough volume to be useful in your downstream process... and if your downstream process is human scale, then you're PCR reaction needs to be as well.
Oh, and finally the actual PCR bio-chemical reactions take a finite amount of time to work, so you can't really temperature cycle by the kilohertz. Probably the fastest you can take it is... dunno, 10 seconds per cycle? The literature is a little weird here.
Very common. I do it all the time.
It was really cool to rub your fingers over it - it made a kind of haptic feedback device as your fingers froze and unfroze from the plate.
It did require kilowatts of cooling on the backside of said peltier plate...
Also, some primers really do not cooperate at fast cycle speeds. PCR is really quirky even in optimized conditions.
The large thermal mass of the heating block in a traditional thermocycler vs the relatively tiny masses of the samples inside the pcr tubes contained within means that the samples are basically always at the temperature of the block, which means the control loop for the heating/cooling system can be modeled and controlled with just a PID feedback loop.