I think you’re kind of answering yourself. Using the more correct quad/hexa/octocopter means the additional work of counting rotors, the annoyance of inevitable pedantic corrections when you get the number wrong, and the realization that you can’t use 'copter as a more general term for the category because the name is taken.
Drone is no more “correct”, but it’s already in common use in many languages so people will know what you mean much better than UAV or whatever. And so it goes.
