I wasn't judging Against Me! on how mainstream punk is. As I said, there are some very good bands from later on. But the point was about how punk has not been relevant since the late 70s, as said by Crass. Crass were the last truly great punk band, because they saw it as it was.
The problem with punk is that a lot of it was very leaden and simplistic in its ideology. People like Henry Rollins, Jello Biafra and co. are much smarter people than the music would suggest. The determined unpretentiousness of it which had been one of its calling cards (musical simplicity, DIY ethic and art) eventually begat pretension, in the form of snobbishness about the values and ethics of various bands (and the whole 'selling out' mythos). Why should I care that one band is more DIY if the other one writes better songs? I'm not saying that you yourself are guilty of this, but I've met plenty of punks who've been like that (and there are plenty of élitist people like that in most genres - I've certainly been one myself at times).
I'm not necessarily fetishizing the classical punk bands, but rather pointing out that punk is an inherently limited genre. The bands who are influenced by the continuing punk bands after its initial explosion into the mainstream... most of them only grow into the self-contained scene that is modern punk. There are still smart guys in there, but they're increasingly preaching to the choir. Scope for innovation within the genre is limited because of its wilful self-restriction.
Public Image Ltd. were more innovative, creative, eclectic, intelligent and better than the Sex Pistols. Truth be told, post-punk as a genre I find more eclectic, innovative and rewarding, and thus my interest in punk after 1979 wanes quite a lot. There are still great albums after then ("Damaged" and "Fresh Fruit for Rotting Vegetables" to name but the two most obvious) but punk became increasingly stagnant and static.