I think that Bruce basically lives in Stark Tower for a lack of anywhere else to go. I think Steve and Clint and Natasha all have their own places, but they go to Stark Tower when an op went wrong and they need to be arond people, or when Pepper invites them for dinner. Or for other things like that. They don't live there, but they go there sometimes to be around other people that aren't SHIELD but who they don't ahve to pretend with.

(because I didn't get a vibe beyond 'commanding officer and snarky field agent' in Thor) Hell yes.

I like the idea of Clint having a strike team. How does Natasha fit in with this?

As to Natasha... I can see both those. I mean, I still like the idea of Clint and Natasha and Coulson being awesome friends and all, but I can totally see that. It's a very valid point.