Less reliability in terms of more moving parts.
Thermal efficiency of diesel engine is around 32%, whereas turbine engines are at 40%+. With same fuel caloric value that is less power / more fuel.
More torque is hard to benifit from when the transmission is the limiting factor.
I doubt it will be all that cheap, maybe at first. Looking at diesel cessnas, at first maintenance was very cheap but now its getting more expensive than conventional engines.