Bunglerat
All to do with engine handling.
Your average PT6-42 or 60A engine comes with a price tag of around USD $1 million. One bad start can cost a fortune. A good turbine operator will ensure batteries meet minimum starting capacity, fuel cocks opened at the optimum RPM, acceleration is normal and ITT’s within the parameters. Cross generator starts will be managed to ensure the starting engine operates below temperature and the operating engine parameters are within limits. He/she will have a good knowledge of the emergency procedures should the start go wrong. Shut-downs will involve temperature stabilization.
Such engines are attached to an expensive airframe and avionics suite equivalent to about ten good Chieftains! You dismissed the speed issues but they are important and become a major event on short sectors. At altitude tailwinds of 100 kts or more further reduce time in the cruise to plan descents and arrivals. Also descents may normally occur at 200 KIAS and a couple of thousand feet per minute. The aircraft will probably have more complex systems, pressurisation, avionics, be operated in an icing environment and take considerable more skill in performance variables.
In our organisation, after endorsement, it takes about 50 hours ICUS interspersed with 50 hours RHS to become single pilot proficient on a B350 engaged in single crew operations. This is followed up with a recurrency course at FSI Wichita. So for the first 100-plus operational hours the pilot is drawing a salary but not contributing!
I guess most operators cannot afford the risk and expense of inexperienced turbine pilots regardless of their piston qualifications.