In modern turbines fuel economy is not that bad - it can be actually pretty good, but those are large ones for small fast starting power plants. I don't know about the small ones. Still they use turbines in turbo prop planes, so efficiency should not be that bad.
Another problem with turbine engines is that they are relatively slow in reacting to power changes. So likely less responsive than an old diesel engine, though better than steam power.
An advantage of a turbine is that if well made there are little vibrations and a long service life is possible.
There is a small chance we might see the idea of a turbine engine in a car again, as a range extender / generator in a hybrid. This would also save the gears to bring down the high RPM down to a street level.