In Romance, the anti-hero has been around since the beginning of the genre. I'm old enough to remember the rape romances of the 1980's, where the heroes were just plain brutal, selfish men who should have been jailed. Instead they met the heroine, took one look at how beeuuutiful she was, fell in love, and turned into loving great guys (and I have a bridge for sale in Brooklyn). Those books put me off the genre for years, but obviously they were popular and the trope still is.
I got the impression that when the audience for that stuff began to diminish, it moved into the paranormal, where the selfish brute couldn't be judged for his actions because he wasn't fully human. Nowadays it seems to have moved on to bigger and better human brutes like world-class assassins.
I don't read those kind of romances and maybe I'm just avoiding the same in other genres, but I don't feel like I see a lot of it in thrillers and mysteries. If you label as an anti-hero the kind of guy who has military or similar background and fights the bad guys tooth and nail, including killing, you could say so, but I don't count those as anti-heroes.