It's all about control. They demand control over servers, not allowing you to self host. They also demand control over communities, by putting them all in one big server or other controlled channels (but sometimes refusing to properly moderate them like in league of legends).

Now, they want to control your device.

That would require them to run more servers, any extra CPU time is an indirect cost. By moving anti cheat to the client (along with other stuff like hit detection,) then they are only spending the customers CPU time not their server CPU time.

It's about money.

In basic terms, your computer has to say something like I clicked here, to send it to the server and orchestrate with the other clients. On the flip side the server sends stuff back that your client can show you were the other clients are. All this raw data can be used by a cheater however they want. If we minimise the data available to you or a cheater to be the levellest, that would be the client only sends mouse and keyboard inputs, and all the client gets back from the server is pre-rendered frames. Think game streaming, from a cheating perspective is the problem solved? No, they just make a program to read screen and move the mouse when it sees an enemy faster than any human can, or more realistically to avoid that detection, just act slightly better than the cheaters opponent. As other comments have mentioned, game streaming for everyone would be expensive for the server. And if your clever you'll realise that even BIOS level detection won't stop a separate computer with a webcam doing keyboard mouse emulation, hence the comments about the developers wanting control. AI deepfakes can attest that even gameplay moderation will get more difficult as the input emulation gets more human like.

So the only hope is to do enough of all these things so that cheaters deem it not worth the effort/not profitable enough.