So it begs the question, why are there no small turboprops in the 100-300hp
range for use on GA aircraft?

Cost. I believe even the relatively small turbines are two orders of
magnitude more expensive than the piston engine of the same power.
Turbines tend to have parts made from exotic metals that aren't
straightforward to manufacture. Also, small turbines are markedly less
fuel efficient than a piston engine of the same horsepower (especially
at the altitudes we fly at).

If it wasn't for the exhorbitant cost of a new turbine, I'd far prefer
them - easier to operate, cooling issues aren't as problematic, and with
modern electronic control I'm sure that operating one can be made
damn-foolproof, not just foolproof.

I'm ignorate of the technology, but seem to remember the airlines went to jets
because fuel costs were lower and they were lest costly to keep running.

If they scaled down well, I expect we'd see them in hybred cars long before
they'd be in general aviation aircraft. You don't need rapid response times in
a hybred, but the 'spool-up' time in a small plane could take a lot of getting
used to by pilots who need lots of throttle jockeying to land their airplanes.

I take that back -- it wouldn't take a lot of time, there'd be aluminum junk
that used to be airplanes near the approach end of lots of airports.