For series hybrids/range extended hybrids, I dont see why gas-turbines arent used more. Automotive turbochargers last plenty long with minimal service. Add a combustor between the compressor and turbine, and in the exhaust stream, put a power turbine geared down as needed to run a generator. Turbines arent good with rapid changes in speed and would be more happy turning on, running upto one speed, and sitting there for a while. Perfectly suited for a range extended electric/volt-ish vehicle. No need for the engine to run at anything other than 100% Its a mature technology (See gas turbine electric plants) and obviously more efficient than diesel piston engines, hence why its preferred for big turbines. Throw some R+D and scale of economy at it to make vehicle size ones commercially viable. No need for wobbly pistons or other arm-wavy mechanical things.
I agree that there is potential for turbines in hybrids (investment is made into small turbine generators
http://www.imeche.org/news/engineering/british-firm-wins-funding-for-micro-gas-turbine-car-engines)Main advantage of of jet powered generators are power per weight ratio (main reason to use jet engines in air planes).
However, there are many problems to be solved. Low weight is an advantage, but that weight can accommodate more total volume (inlet, outlet, heat/noise isolation) than conventional solution.
Jet powered turbine generators are a bit more complicated than you describe - they have many moving parts, more than equivalent piston engines in case of more powerful units (part count increases because of compressor/turbine construction). Small jet engines use monolithic shafts of high precision, high quality bearings, oil and cooling systems - reliability issue comes to mind.
Also, precision and custom parts quickly adds up in cost. Big part of appeal for hybrid car is it running cost and price.
IFRC, British engineers constructed small jet turbine for Jaguar(10-20 years back), but it was not implemented at that time.