Hey so good news and bad news-- the bad news is that, yes, cheating has taken over most FPS games, and that IP address bans still aren't a viable option to stop them (IP addresses can be spoofed, after all, as can most HIDs.) 
The good news is, as you said, there IS a way to program a "true anti-cheat" that will auto-detect anomalies not only in a specific player's gameplay compared to the rest of the playerbase, but be able to detect anomalies between sessions of their own gameplay. AnyBrain is a collaborative AI project which uses artificial intelligence to build a profile for each gamer it encounters. It tracks movement, aim, positioning, and your actual stats themselves to build a firm understanding of the way EACH individual plays. Once it's done that, it is then capable of detecting that SPECIFIC PLAYER in any game they play with AnyBrain enabled; this means that cheaters can be banned the instant they start cheating (AnyBrain is also trained to recognize obvious instances of cheating, too, to be clear). Having to rotate accounts per-match, or spoof a new HID or IP per-match, strikes me as an inconvenience most cheaters aren't willing to suffer.
 
Best news yet is that nearly every major developer has already started backing the project.