And realistically, some real non-cheating players will by chance just have similar statistics to bots, especially since the bots will start doing their best to mimic real players.
Also many players don't need to cheat all the time; just in that critical moment when it really matters. Didn't Magnus Carlsen say he only needs a single move from a chess computer in the right moment to be virtually guaranteed win? Something like that probably applies to a many people and fields. This is even harder to detect with just statistics.
Also also reminds me of the "you can't respond in less than 100ms, and if start the sprint faster than that after the starting pistol then you're disqualified"-type stuff they have in the Olympics – some people can consistently respond faster and there's a bunch of false positives. Not great.