I would not have called him an anti-hero so much as a reluctant hero. He did not go out patrolling for wrongs to right. He just found himself fighting against Evil with a capital "E". But having found himself fighting evil, he did not back down. It was an interesting theme that has been visted many times (Dr Strange, the Demon Etrigan, Ghost Rider and the Son of Satan, then Hellboy and Spawn and even Buffy the Vampire Hunter and Angel) but none really successfully. I think the most successful was Bufy the Movie where she re-evaluated her previous shallow life in the light that there really was a supernatural evil out there. I suppose they think that the issues raised are not appropriate for children's comics.
As to why they are so popular, that is easy. It is because they are more like us. That means that when they act heroically, so could we. We think "Hey they are just like us so we could be just like them, given the same circumstances."