Validating input and physics is easy and is effective against some of the crazy cheats people ran on eg PUBG. But it’s much harder to “limit information”. For example in CS if someone is 95% hiding behind a smoke screen with just one foot sticking out, do you tell other players about this player or not? If you don’t, then you are depriving them of information they should have been able to see, if you do, then it still gives a cheater an edge because even if you do spot the foot you will probably have a hard time actually shooting at the player because his body is still hidden.
And even if you can 100% accurately decide when to hide or show information or if you are outright just streaming the game to the players there are still cheats that you cannot detect this way because they only enhance player capabilities within what is possible for an honest human player. For instance a simple cheat can detect if another player’s head is under your crosshair and fire automatically (with a randomized delay to game anticheat systems.) Realistically cheats these days are more complicated and do way more to emulate human input. It’s not easy to conclusively tell if a player is cheating thus way or not just looking at his inputs in one game. Maybe he is just fast, maybe he has lower latency, maybe he is just pre firing at spots he knows an enemy is likely to come from. You can’t know for sure unless you know what’s actually going on on his PC and his peripherals. And if you start banning people using just statistics you will likely end up with many false positives.
At the end of the day there is no silver bullet to cheating. Even if you fully control a player’s PC there are still ways to cheat in hardware [1]. You need to find the balance between annoying too many players with your anticheat and your game getting overrun by cheaters.
[1] https://www.counter-strike.net/newsentry/6500469346429600836