I worked on a study of turboprops for small aeroplanes a little while ago. It's all proprietary data (sorry) but I can give you a few bulletpoints:
- At GA speeds, piston engines are much more fuel efficient.
- But AVGAS is much more expensive than AVTUR
- As a result, you roughly break even on fuel costs per hour and on payload (the engine becomes lighter, but the amount of fuel you have to carry becomes greater). If however they start taxing AVTUR anything like AVGAS, then all bets are off and the GT engine becomes much more expensive.
- There are some small turboprops out there in use but nothing certified - they're all in use on amateur built/experimental aircraft.
- The killer however is noise. It's almost impossible with current technology to get a small enough gas turbine engine, quiet enough to be socially (or in some countries such as Germany legally) acceptable. The best fix is probably to try and deflect all the noise upwards, but nobody's really tried this yet.
Incidentally, I think that Rover (British now-dead car company) built a gas turbine engined car in the 1950s or 1960s; I'm pretty certain I've seen one in a museum somewhere, but couldn't tell you much more than that.
G