The main issue with small turboprops is fuel efficiency. At best they use about 0.7-0.8lb/BHP.hr whereas a Lycoming is about 0.45 and a good turbo diesel can get down to about 0.33. That's about 20% overall energy efficiency for the turboprop against 30-40% for pistons. Electric powerplants can get nearer to 90%, but need much higher energy storage densities to compete. There are several promising technologies in development so expect advances before long.Turbofans and pure jets are even worse below about 0.4 Mn and can be very noisy.
You can trade some of that high fuel consumption for the light-weight powerplant, high altitude performance, reliability, fuel availability and low flamibility.
With the high initial cost and all those issues, it simply doesn't make sense in our end of the GA market.
There was a recent attempt to make a small turboprop with the
and RV-4, but development costs and problems killed that. Cheapest options at the moment are offerings like the Walter 601 at about £80k.