It occurs to me that compared to a piston engine, the turbine is 1) more
expensive, and 2) more reliable. But, why are those things true?
Looking at it another way, is there some inherent reason why piston
engines are cheaper to produce? Is there also some inherent reason why
they're less reliable?

If I were to give you the $/HP budget a turbine designer has to work
with, would you be able to design a piston engine that was as reliable
as a turbine?