[1] https://www.youtube.com/watch?v=HUEvRyemKSg
And now we're going to get OS level DRM that works through all of our browsers, thanks to Netflix, Google, Microsoft, Apple, and last, but not least, the W3C. Terrific.
Often the intent of a cheater is to ruin the game for everyone else, with patches that give them super-powers (aimbots and wall hacks are pretty common) and the ability to unfairly dominate the other players. Sometimes there are cheaters in official tournaments (a high-profile player in Germany was recently found to be cheating).
Scanning a whole system for "DRM cracking tools" seems very, very bad to me. If this is what EA is doing then they had better have a really good explanation.
Scanning a the running environment of an online game, under the umbrella of a EULA, seems fine. I'll note that if you object to this, you're free to play on non-protected game servers.
Some games are designed to be inherently cheat resistant. One strategy is for the server to never give the game client enough information to be useful for cheating, so even if you've written a totally cheaty client it doesn't do you much good. (Reductio ad absurdum, your client is just a smart video feed with some controller input).
Cheaters suck, but they're a fact of life and if your online game doesn't prevent them then you'll be overrun by the scum and honest players will stop playing.
Or?
"I'm going to pout and not pre-order Battlefield 5 until a week before it comes out. That'll show them!"