Turbines are lightweight and small, but their fuel consumption is normally quite a bit higher than gas (or diesel) engines for a given horsepower rating. Hybrid technology would help somewhat with sluggish acceleration and would allow the turbine to be optimized for a given power output. However, you could do the same thing with gas or diesel engines, sort of like a diesel electric train. The approach is to use the engine to drive a generator and produce a steady power output with batteries providing supplemental power for acceleration and peak loads. Wheel motor/generators could be used to provide all wheel traction and eliminate the need for a transmission, but I don't know how they hold up under long term use or how much they cost.

Honda and Toyota have taken two different approaches to hybrid cars. I'm not certain about the Honda Insight, but the Civic and Accord hybrids use a small electric motor (~15 horsepower) to provide additional acceleration while everything else is handled by an essentially conventional gas engine. The hybrid Accord only gets slightly better gas mileage than the conventional Accords, but the performance is improved. Toyota's Prius has an electric motor that's almost as powerful as the gas motor. It uses an infinitely variable transmission and some sophisticated electronics to balance battery state, charging levels, and energy needs from both the gas and electric motors.

I think a constant output motor optimized for average power levels would be a more efficient design, but then Honda and Toyota have some very good engineers who decided against that approach. It might have been for some sound engineering reasons that I don't know about or it might've had more to do with production economics. Either way, it shows my thinking may be flawed. I've love to see some test results to find out.