It is not a question of lacking good alternative, it is a question of lacking good solutions. Games like FPS that emphasize fast clicking can always be defeated

It is not a question of lacking good alternative, it is a question of lacking good solutions. Games like FPS that emphasize fast clicking can always be defeated by anything that can emulate clicks and keypresses and see the display. If you take the problem to the limits: a camera looking at the physical screen and a robot actually moving the mouse and keyboard is going to be able to have users cheating. You simply need a reputation system. Allow people to vote on someone being a cheater or simply refuse subsequent match with them.