If it is only as good as a real player than it won’t be invincible and will be equivalent to playing with a few AIs in a multiplayer game - which already happens.
Also, I believe the exact mouse movement will not be the same for a human and an aimbot - so not only statistics can be used to ban players
So you have two choices here. You either ban the best players or the aim bots just behave with a success rate close to the best players.
And when I'm talking about statistics here, I'm not referring to the kill/death ratio, but rather all input data received from a cheater.
I recall seeing players hovering in the air and spinning while shooting rockets out at hundreds of rounds a second. There was also a way to modify your files such that you could crash a game just by joining it. The experience was as interesting and fun as it was awful.
I get the sentiment here but we're specifically talking about a mechanism specifically designed to detect other software that is used for cheating.
The alternative is a world where games will only run on machines with SecureBoot, a signed kernel with kernel security on, and only whitelisted signed modules.
There isn't a good solution for how to run games where the clients have to be semi-trusted on a hardware and software stack controlled by the user. If you give me total control over the environment in which a program runs I can make it do and believe anything.