One thing that hasn't been mentioned yet is that although gas turbine engines have an excellent power to weight ratio, they are less efficient than piston engines of similar power output, especially in small sizes.
Gas turbines typically use only a third of the oxygen in the inlet air, or to put it another way, they ingest three times the air required to burn the fuel. This is because the hot parts of the gas turbine (especially the turbine blades) are subject to constant high temperature and would melt if the minimum air required for combustion was used. On the other hand, gasoline engines use the minimum air required for combustion (as do diesel engines when operating at full throttle.) The combustion temperature in a piston engine is therefore higher than in a gas turbine, but it does not damage the cylinder walls because they see only the average temperature of the full cycle.
The low flame temperature in a gas turbine limits the theoretical Carnot efficency. Because the gas turbine uses three times the mass of air required for combustion, a lot of energy is carried away in the exhaust. A more detailed analysis will show that these two statements are more or less equivalent.
Thus a truck diesel engine can achieve 50% efficiency (with the help of a turbocharger) which is unheard of in a gas turbine. Combined cycle power stations achieve better than 50% efficiency by raising steam from the exhaust gas of gas turbines to extract extra energy. A typical mass balance is: 100MW fuel, 40MW shaft power from the gas turbine, 40MW steam raised from the exhaust, 20MW lost to the chimney. The steam raised can then be used to generate electricity at 40% efficiency, yielding another 16MW. Total 56MW electric from 100MW fuel.
Installing a combined cycle plant in a car (or even a truck) is prohibitively complex. Therefore, piston engines offer better efficiency.
This is especially the case in small sizes. Better efficiency is achieved by high combustion chamber pressure. But the pressure that can be developed / recovered by a single row of blades is proportional to the square of the blade velocity, which means that rotors in small gas turbines have to spin very fast or have many rows of blades on them in order to achieve decent combustion chamber pressure.