When the anti-cheat runs on the client workstation, it just tries to make sure the client isn't doing something nefarious. It's cost effective for the game company and doesn't cost the end user much except compatibility

To do it on the server, you end up needing to run a full simulation of the game which is really expensive at scale. You can, to some extent, just look for input values and thresholds, but over the years of trying to do this, people always find ways to cheat input threshold monitoring.

An interesting take is making the end user run the client on a rented server, then they can both have the client remote and not pay for anticheat at all.