Most quadcopters aren't gas-powered because they rely on rapidly adjusting the speed of brushless motors attached to fixed-pitch props to control their attitude.

A few hobbyists have built gas quads with variable-pitch rotors, but the amount of mechanical complexity and hassle involved makes a similar nitro-powered single-rotor helicopter more appealing for most hobby applications (stunt flying etc).

As more novel designs that don't rely on precise motor speed control (for example, this one) come into play, I think gas motors will make a minor resurgence as people rediscover the energy density (and therefore flight time) they can achieve.

However, for most hobbyists, electric just makes more sense. It's usually quieter, works indoors, is generally a lot less of a pain in the ass to deal with (no need for starters, glow plugs, choke, adjusting mixture, engine maintenance, etc.), and is usually less heavily regulated.

Why not hybrid? Have an onboard gas generator to recharge the batteries. As soon as the gas runs out, the drone has X min of battery flight time left to get back to solid ground. No need for mechanical complexity.

There's an MIT spinoff called Top Flight that was working on a hybrid quadcopter, IIRC. I think the main reason you don't see them in the hobbyist space is size floor (you need a pretty big machine to make the weight overhead of the motor, generator, and charge circuitry work out) and money.

Hell, you could have a small buffer ultra capacitor or battery providing the motors with electricity while a gas engine at constant RPM recharges it. The whole system would have to have a very high conversion efficiency though...

Gas engines could be coupled with one or several CVT transmissions?

I think you could just use the simplest form of CVT: a variable-diameter pulley under each rotor. You'd still pay a pretty big cost in terms of mechanical complexity, though, which makes the swashplate system more appealing as offers a lot of additional advantages in terms of thrust vectoring.

For multirotors it's just very difficult and impractical to power them with gasoline engines. If you were to build a gas powered multirotor, you'd have to have a central engine connected to each motor by means of some complicated mechanical linkage. This would also mean you could no longer control the speeds of the motors individually, so you'd have to achieve lateral movement by pitching the propellers, like on a helicopter. All these things mean that it simply doesn't make sense to build a non-electric multirotor, it'd be massively expensive and inefficient you'd be better off going back to a helicopter.

In terms of fixed wing drones, the benefit of electric over gas is mainly ease of use I believe. It's a lot simpler for someone to charge a battery and just plug it in than it is for them to fill up canisters, refuel the engine and cope with the complexities of tweaking and starting an engine. That extra effort and learning curve isn't worth it for the slightly longer slight time.

For aerial mapping the go-to option is normally fixed wing drones, they can easily achieve 30-40 minutes of flight time and this is normally enough for those kind of applications.

For a coaxial, cyclic controlled UAV like this you could convert to using a fixed RPM gas engine though.

Control and cost.

PWM motors can control their rotation very precisely unlike IC motors. That is one reason you see multicopter designs nowadays. You can quickly alter the torque. I didn't see how this design alters pitch or roll, but I know there were some coaxial experimental designs that can alter the torque in a single rotation to affect those axis. That is simply not possible with something powered by burning fuel. It might be possible to have a mixed system, using an internal combustion engine for primary lift and electronically controlled steering, but that would be a more complex system and the benefit isn't abundantly clear.

Size, noise, maintenance, predictability, simplicity, cost. Haven't seen a power/weight trade study of batteries vs engine+generator+fuel, but it may be closer than you think. There's a lot involved in a ICE power plant, and even if it did win, it'd have to be a pretty big machine compared to your average multirotor due to minimum scale on gasoline engine components.

There might be a market for large endurance multirotors, but apparently it's not obviously attractive.

Price and safety, I would bet.