Ruin Explorer
Legend
I think the part of those movies that makes them sell so many tickets is the johhny depp part, and not so much the hero or anti-hero bit.
Also, what's her face is hot.
Johnny sells a lot of tickets to any movie, but Jack Sparrow sells more than Johnny normally does, and this is because it's such a wonderfully insane, over-the-top, larger-than-life character who is not just a "good guy".
If he was purely heroic, he would be far less interesting and far less broadly appealling. I mean, imagine Johnny Depp playing Orlando Bloom's role. You think as many tickets would have been sold? I'm telling you, they wouldn't. Equally, without a good guy to balance things out and act as a "straight man", I don't think Johnny's role would have worked so well. So both worked in this case.
The key to understanding the broad appeal and international success of PotC (which cannot be attributed "Pirates are cool!" alone, as every other pirate movie in the last thirty years has been fairly unsuccessful) is that whilst virtually every character, from Elizabeth Swann to Lord Cutler Beckett is "morally compromised" on some greater or lesser level (possibly excepting Will Turner), they almost all have some kind of redeeming feature or likeable trait. This potentially increases the audiences emotional investment in what are, otherwise kind of lengthy, semi-nonsensical films, as they identify with both heroes and villains, and indeed the last Pirates films makes great play of a sort of shell game with who is "good" and who is "bad" and what exactly is going to ensue, who is going to backstab who, etc.
Hussar - Well, exactly. If someone doesn't think Jack Sparrow counts as an anti-hero, they probably should avoid using the term or trying to understand why others use it. Jack Sparrow is likeable, not particularly smart or good. He's basically a human cat, in that he doesn't love anyone much, but is good at faking it for benefits, tends to fall on his feet, and makes his mistakes look like intentional decisions. He's certainly also got a strong degree of "low cunning", but not really much in the way of genuine cleverness. If you hate cats, you probably hate Jack Sparrow.
The days of angsty '90s emo "anti-heroes" are long gone, but that doesn't mean that are no more anti-heroes. Quite the contrary. Indeed, if anything, the general boundary between hero and anti-hero has become rather more blurred.