The problem with a statistical method is you can't ban the best players. For most cheats, you can dial the cheat down until it's at a human level.
The main issue, I guess, is they’ll have lopsided aiming proficiency (due to the boost) vs game knowledge. But that’s basically a crapshoot anyway in mass-market “competitive” gaming.
Games "feed" less skilled players to higher skilled players - just enough that the less skilled players don't ragequit. Higher skilled players don't actually want to play in a lobby full of people their skill. They want a few people their skill, and then a lot of people they can stomp.
<Bitterly laugh-cries in Rocket League>
This tends to stand out like a sore thumb once you start looking at things from the perspective of the frequency domain. Even if you use an RNG to delay activity, the properties of the RNG itself can be leveraged against it. You may think taping a pencil to a desk fan and having that click the mouse button is being clever wrt undetectable RNG, but you must realize that the power grid runs at 50/60hz and induction motors are ~fixed to this frequency.
There is also the entire space of correlation. A bot running on random pixel events with perfectly human response times, while appearing "random", is not correlated with anything meaningful outside that one pixel being monitored. You could check for what are effectively [near] causality violations to determine the probability that the player is actually human.
I’ve thought that trying to make a bot for personal fishing use would be a delightfully fun project, and this is how I pondered evading such anti-cheat heuristics.
> A bot running on random pixel events with perfectly human response times, while appearing "random", is not correlated with anything meaningful outside that one pixel being monitored
So would a human who is tunneled-vision at the center of the screen.