Earlier quoted context omitted.
I think that there are very few tasks in competitive multiplayer games that humans perform better than machines[1], I don't think your statement holds true unless you exclude a huge amount of game genres or you take all the fun out of them. (E.g. no FPSs or ..FPSs with no aiming?) [1] Unless we're talking about captcha solving competitions, for now, maybe. :)
You're right in that, if your server rejects inputs that are too fast, too precise, too robotic to be human, bots will emulate the top-playing humans ever more closely. But the question I want to ask is: Is that a problem? If all the bots and cheaters are playing indistinguishable from high-level real humans, where's the harm? Or, to quote Westworld: If you can't tell the difference, does it matter?
You don't have to reach pro levels, it often only takes small assists to turn a balanced game on its head, ruining someone's experience with a game. Repeat often enough and the userbase will leave, feeling cheated or at least demoralised for being unable to compete or improve.
And allowing machine-assists, thus leveling the playing field, turns the game into a completely different one that is (imho) drastically less fun whoever may not be interested in (or may be unable to) running/coding their bot.