My POINT is that LOTS of films are heartfelt.
To me I'd say that moment in AVENGERS is Caulson's death. Here we are throughout the whole film enjoying seeing these guys fight. Enjoying seeing them bicker. Seeing good guys bicker. Pessimism winning out. But, when Couslon dies - I think that moment hits the audience just as much as it hits the characters. Not because we got to know him (but that too). But because of what Coulson stood for - he stood for optimism in a dying time. He believed that heroes and that good could still exist, and here we were before enjoying seeing that get torn apart and having a good laugh at it only to be hit in the face. I'd say it had an impact not just because of Coulson, but because of the importance of his beliefs and outlook that we lost in this world and that we do need to continue going at it as we should be.
As for politics, I don't know... I'd say the whole "you're a people meant to be ruled, and unset without a ruler" was pretty spot on and a harsh criticism to make.
BASICALLY I'm saying if you look, you can find those things in pretty much every film.
GRANTED The Avengers was more SOCIOLOGICAL than POLITICAL.