You seem to be suggesting that the cheat detection is just a performance thing? It's not.
There are some forms of cheating that can be detected at the server level, and they probably are. You fired more ammo than you've got? You defied gravity in ways that the game doesn't allow? You took fatal amounts of damage but never entered the code path for death on the client side? Your aim is absolutely 100% flawless? Those sorts of things they can probably detect at the server level.
But there's a bunch of cheats that the server can't detect. You've got a mod that lets you see through walls? That highlights enemies so they'r easier to spot? That shows secrets that your client is aware of but isn't supposed to show you? That looks at what's on the screen and nudges your reticle over towards the face of your enemies without making it obvious? These things generally need to be detected on the client machine.
Now, if they were rendering the entire game at the server and displaying it back -- like you seem to be referring to with PSO2 -- then they wouldn't need to scan that for cheats, because all that code would run on their own servers and be untouchable -- but that is *not* how most people want to play FPS games, especially those who are playing competitively.