Very small gas turbine engines run into efficiency issues because of the fact that the flow through the fans, combustor and turbine must end up in a thinner and thinner ring. Even as you shrink the outer case diameter, you still end up with smaller and smaller blade heights. As that happens, the amount of the blade in the boundary layer in each case gets larger and large, and ghence less efficient. Whereas a piston-type engine is far easier to "scale" because the compression is fundamentally mechanical, not as dependent on efficient aerodynamics. So small gas turbines are always going to be relatively inefficient.
Things like small RC aircraft engines, and missile engines, can put up with the efficiency loss because they want power density - the model aircraft is constrained by the desire for scale respresentation at a sensible overall size, the missile by carriage and tactical considerations. But on a vehicle like a small GA aircraft, where volume or cross-section aren't at a premium (certainly for the kind of power outputs that make sense) there's no sense in having a tiny inefficient gas turbine when you can have a more efficient piston that doesn't drive the design size anyway.
My two cents.