Turbo prop engines typically have higher fuel consumption per hp produced than piston engines. As they scale smaller this gets worse. The term for this is the specific fuel consumption (SFC) which has units of lbs/hp/hour. Think of it this way, how many pounds of fuel does it take to 1hp for 1 hour? (there is also a metric version but lets not go there). A lower number means that the engine is more efficient.
The table below shows a range of SFC for turbo prop engines. Note that there is a trend in the data where the larger engines are more efficient. It is important to note that this is due to both limits of physics and engineering. While these numbers can always be improved on it would be naive to think that a major jump in performance can occur without the development of some improved materials and production techniques and even then the increases might not be that large. Just as a bumble bee that is 1000 times bigger than a normal one wont fly, a small turboprop wont ever be efficient.
Engine SFC lbs/hp/hr hp
Wren 44, 2.5, 7.5
Solar T62, 1.1, 160
RR500, 0.62, 475
PT6B-36A, 0.58, 995
Say you tried to design a 100 hp turboprop and say that you could get the SFC down to 1.0. That would mean that you are burning 100lbs of fuel per hour at maximum output which is about 56l/hour. Not a cheap proposition compared to a Rotax or Jabiru....
It would sound cool though....