People have used fuel-powered drones extensively before Li-Po batteries got good (including me). My take on why they haven't taken off as much as the modern quadcopters: they are quite a bit scarier.

The main two types of flier before quadcopters were fixed-wing model airplanes, and helicopters. They are both riskier to use than quadcopters: fixed wings can't be stationary and need a large area to fly around, while helicopters have large dangerous blades. This is why either of these are less attractive to the mass market.

On the flip-side, I think converting a quadcopter to use an engine is expensive because controlling 4 blades at once is not as simple as with 4 electric motors. Either they need to have 4 gas engines (expensive, not as responsive as electrics) or they need to have a variable pitch mechanism (now you need an intricate/expensive mechanical system of levers and servos to transfer the control).