Game servers are incredibly expensive, and server side anticheat is more costs.

Whether or not the studios can afford it (they can.) is irrelevant, it's simply cheaper to go for flawed client side because the client will do most of the processing.

Any software developer worth their salt simply does not trust the client, but management is gonna manage and the engineers have to come up with a solution to "we must have anticheat because we said so, and you must keep server costs per user below x". It's easy to forget that most implementation choices in video games aren't made by developers who like games, they're made by middle managers who view games as a money-generaring industry.