usta in Portland
"Aren't some navy ships run exactly this way-or maybe used to be? Are they just too difficult in terms of heat and emissions or something?"
Indeed they are, just about every decent Navy uses them as does the new Queen Mary ( but her turbines are the latest evolution )
The General Electric LM2500 gas turbines are for example in Oliver Hazard Perry Class Frigates, run 2 x of these sucking F76/JP-5 ( marine diesel -ish ) to push them along at 'over' 30 knots. Been around since the 70's in the Spruance and Kidd class destroyers.
Not great when mated to an electric generaor with a thermal efficiency of about 40 percent at ISO conditions.
Small and compact APU's ( auxiliary power units ) happily live in helicopters are are the first turbine to run up in lets say a Skiorsky S70B helicopter to run the electrical system to get the two main turbines to light up. Running jet fuel ( fancy kerosene ), jet powered passenger aircraft tec have similar systems.
The turbines get a little sooty in use and we used to perform the 'water wash' procedure where water in injetced into the running turbine to clean thenm out. Not sure how you would do this in a Hybrid passanger car, wrong amount of water and it gets nasty.
Engine Hours are a recomendation based on a lot of historical data, vibration is the thing to watch. Having seen a LM2500 let go it makes the otto cycle engine term "spun a main bearing" look like a picnic.
Little APU type turbines are well developed and a mature technology, my thougts are that car makers think hybrids need some 'planned maintenance' items for the motor trade to repair to make a few dollars on at a periodical basis - ie oil / filters spark plugs etc.
Never imagined that small scale APU's would ever end up in passenger cars. At the small scale heat could be managed - thermal efficiency, I just don't know.