I think some of the recent comics have taken it too far, where Hulk is a nobler wiser more in control entity than Banner, and more powerful than some cosmic beings... but the idea that they're the same guy makes a dramatic amount of sense, and thus the relationship, the metaphor for dealing with one's rage has to be deeper than 'stay away.' A character who's only real problem is this uncontrollable monster... if they receive any character development, will gain some control. The MCU has handled that balance well, Banner can point the thing, but you never get the idea that this is not a menacing force of nature that can't really be controlled.
In a universe by himself, Hulk as a monster makes sense, and can go on indefinitely, but in an integrated story world, a monster is just a villain. Now, you could write Hulk as a villain the Avengers fight, an anti-villain of sorts, as the person behind him doesn't want to become the monster, much less fight, but then that brings up other issues. If a scientist wants to be cured of being a villain... and he has Mr. Fantastic's number... why is he still a monster?
He's not a character that makes sense to 'stray' because he's too much of a factor, too much of a force of nature. He's either against the team or for them. Maybe even both, but there is no neutral Hulk.