Anti-heroes are all over the place in our modern folklore.
You've got the Godfather movies, Star Wars (take your pick: Darth Vader or Han Solo), Dexter, Lock Stock & 2 Smoking Barrels, Many of Eastwood's characters from the spaghetti westerns, and more.
Shakespeare had anti-heroes. Look at Romeo, closely. What about him was truly heroic? But he was ultimately a character for whom you developed sympathy.
Anti-heroes can be traced as far back (off the top of my head) to Beowolf (boastful, prideful, selfish, lusting after another man's kingdom/wife and more). I'm willing to bet there are Biblical anti-heroes somewhere in the old testament.
They make for great post-entertainment discussion. Like we're having now.
They aren't a harbinger of impending societal doom.