Eventually yes but the point is he can always be brought in later. As for Leader and Strategist, you have Nick Fury.
Ummm, you don't see the irony in complaining that Captain America wasn't a founder, and then suggesting Nick Fury covers the role?
As for Moral Compass, Iron Man and Thor have decent working compass so you don't need a shinning light like Cap right now.
Tony Stark, as depicted in the films, is a narcissist. As depicted in the comics, he's lately been well written and interesting, but hardly with a clear moral compass.
Thor's moral compass was first born in his movie, his lack of one was why Odin banished him. Whether it's fully matured is open to debate.