Would the narrow efficient band matter with a wobbly prop?
My understanding was that small turbines were inherently inefficient because of the gap between the blade tips and the outer casing, which becomes proportionately bigger as the turbine gets smaller.
I agree with Adam that there may be a role for turbines in hybrid aircraft - you can do a lot of fun things with electric motors, but the idea of battery powered aircraft has always seemed to me to be a case of 'greenwashing'. If you wanted to spend money on reducing carbon emissions, there are doubtless much better ways of doing it. The other advantage of a hybrid system is that you get electric reliability - which can be phenomenal - leaving a fair amount of time to complete a go-around or find a better field, in the event of an engine failure.