A behavior analysis program based off data could very easily do this with little to no false positives. Essentially it's doing what everyone else is already doing, which is looking for the behavior of cheaters. There was a version of this called 'Hack Cam' which came around almost a decade ago, but got shut down due to various nefarious reasons and nothing has risen to take it's place. It works based off the players behavior and scores them accordingly. With enough data the player can be reliably banned.
Aimbots function like a machine, if the game detects a cross snapping to a bunch of peoples faces in a linear fashion with machinery precision - ban.
If someone is looking at someone through a wall constantly before they ever see them - ban.
If someone is manveuring around someone they don't know is there constantly - ban.
If someone moves to dodge something they shouldn't know is coming - ban.
Constantly going around the map dodging people - ban
There is a lot of behavior that could be easily compiled and then used for this purpose. Valve has databases of players and infrastructure to process and take care of this stuff. There is an example of the above system working that I preserved here: https://www.youtube.com/watch?v=mIfXd-RTiQM
That came out almost a decade ago and the idea and methodology for it hasn't changed, because regardless of how cheats and change and mutate, people don't. The way they interact with the environment and process information does not change. It does based off stimuli, especially off stimuli they shouldn't have access to.
The other option for cheat detection is a completely locked down system and I don't know why console developers haven't been advertising this in spades. This is the ONE area consoles excel at: They're locked down. Meaning it's incredibly hard (not impossible) to cheat on them. They could even be seen and marketed as 'the competitive system', because cheating would be almost none existent. If they took this concept even further I'm sure they could further lock down the systems so it would be next to impossible to install anything on it without their permission, especially with things like soldered on storage. Making it neigh impossible for the average joe, let alone advanced ones to do anything on it. They just need to offer the same experience as on a PC along with the ability to use a mouse and keyboard in all games. This is actually one of the reasons I went from PC FPS's to consoles. It's not worth playing FPS's on the PC anymore, regardless of how good they are.
Locked down is easier to do then behavior heuristics, but heuristics would catch almost all cheaters over time. Locked down would just prevent them up front.