Expensive
Every small turbine engine I've ever looked at were extremely expensive to buy, plus they have to be rebuilt at something like every 2000 hours of use, which is also very expensive. Then there's the problem of the hot exhaust that you can't just blow out the rear of the car like a piston engine.
If the turbine is going to be used to drive a generator then there's not that much of a problem, but for direct shaft to transmission applications the turbines are way too sluggish to develope power, like "Tubo Lag".