Actually, gasoline engines scale down pretty well nowadays. You lose a bit of efficiency, but if you want to have range, they are still your best bet. A small gasoline RC plane
could cross the Atlantic for instance. You can't yet do that with an electrical one (unless you use solar panels of course).
The reasons on why you don't see them in quadcopters are twofolds : First, they indeed are heavier and more complicated. Putting 4 of these in place is harder to do and you need to feed them gasoline, to have 4 valves, this is more complicated. However, on regular RC-helicopters, gasoline engines are very common : a single engine can activate both propellers and there is no need for them to turn at different speeds.
Which brings me to the second point : Quadcopters engines need to change speed very quickly, they also need to stop and start again almost instantly, which a gasoline engine cannot do. You almost need to kickstart it with an electrical engine.
I think quadcopter are much more precise than regular helicopters, but in disaster relief, you don't need precision, you need range.