Ever seen eye-watering price of a new turboprop engine? I think PT6's price (the engine put into most single turboprops) is rougly around half a million €. The next problem with turboprop engines is that they are very inefficient at low altitudes, which is exactly the reason (except helicopters) why they are put into aircraft which tend to be flown above FL150.
About the running costs, as with all things on this world - there are two sides. Turbine engine do have greater reliability and cheaper fuel, but I don't think specific fuel consumption would differ so much at FL100 (for flight without using supplemental oxygen for example) between atmosferic (or turbocharged) piston engine in LOP operation and turboprop. As for the longer life, it's probably true, TBOs are longer, but the price of an overhaul is similary increased, so it's not really an advantage. Of course, if you do 4000 hours a year and would like to have an overhaul every two years instead of twice a year, than turbine is probably the way to go.
Turbine engines are generally more reliable than piston engines, but they are usually operated by much more experienced pilots, which usually keep the engine parameters within limits. Lycontinentals (at least low-powered one found in PA28/38, C172 ...) can be operated almost (well, I wouldn't go from full power Vx climb into Vne dive with idle throttle) in any way and still make it to a TBO with perhaps changing a cylinder or two. Most of piston engines (except some high-powered turbo/super-charged and Rotax under-sized engines) also have equal takeoff (maximum) power and maximum continuous power, which basically means you can fly the aircraft from brakes off to top of descent with all three forward and it is highly likely you won't do much (if any) damage. Besides, most turbine engines require very laminar airflow through the engine to prevent compressor stall (and thus damage), which actually eliminates option to do serious (continuous) flight training with them, such as stalls, unusual attitudes, spins, ...
I think the future for low-powered spam cans are diesel engines, which have relatively good efficiency, they can run on Jet A-1 (this is the real advantage), the ones currently on market have FADEC, which makes them attractive to pilots who don't/won't/can't understand piston engine management. Leave the turbine engines for pressurized aircraft, which can really use them to their full potential.