I think at a few things are keeping turbine engines out of cars:

1. Specific fuel consumption (amount of fuel burned per horsepower) is lower for piston engines than for turbines,

2. Turbine engines are still quite a bit more expensive than piston engines,

3. It might be harder to make the turbine engines meet current emissions requirements.

Jet aircraft use turbine APUs because they're smaller and lighter for a given amount of power produced. Turbines also tend to require a lot less maintenance than piston engines. Also, using turbine APUs instead of piston APUs simplifies the fuel system since the turbine APUs can use the same fuel as the jet engines.

I've wondered why hybrid electric cars don't use electric motors for primary propulsion (say, wheel motors). I'm sure Honda and Toyota looked into them. I suspect they cost more to build than the current configuration. Engineering is often trying to achieve the best results that can be produced for a given amount of money. Cost benefit analysis is a very big part of engineering, especially for a product intended for mass production. A small diesel engine might be a better choice than either a turbine or a gasoline engine.