Why do turbine (jet) engines cost so much more than piston engines?

G force on a big turbine blade spinning at 2200 rpm is going to be considerable.
You don’t want the things flying apart.

G force calculator

I stand corrected

For clarity:
The waste heat is not delivered to the intake air (i.e. the air coming into the compressor), it’s delivered to the air downstream of the compressor section. And it’s not about hot air compressing more readily; it’s merely about taking that waste heat and passing it through the turbine to extract another fraction of it to useful mechanical work. The only way this works is if your compressor outlet temp is lower than your exhaust gas temp - IOW, if you’ve got a gas turbine with a low pressure ratio.