People would want client side checks for variety of reasons. It is more performant (for your server), it is more robust (imagine you are not sending player data that are behind a wall. Now that player might be visible very quickly by moving but your server response might be too late) and some stuff is almost impossible (aim bots etc. Sure your server make some guesses but a client detecting existence of such programs is still a plus)
Suppose we have a competitive game where the goal is to click on a target quickly. Most online shooters have this property.
A cheat can always do this at least as fast as the best players in the world can.
Without client-side cheat detection, you will not be able to detect, on the server side, whether or not the commands sent from the client are coming from a cheat, of a world champion player.
Yes, client-side detection isn't perfect. But in security, perfect is unattainable.
If everything goes through their servers, it seems like a huge waste of time. If it's peer-to-peer it makes sense.
I'm trying to google it and there seems to be a lot of semi-informed lore, some people say it's centralized and some people say parts are p2p.