I think the biggest "benefit" that a dojo can get out of affiliating with an organization is that your teacher gains a teacher. I'm not too sure if I can come up with any other reason why someone would want to affiliate outside of that reason that's "legitimate." And, if I can say so myself, I think affiliating would only make sense if and only if the teacher of your dojo really wishes to become a real
student of the organization's teacher(s).
I think having a teacher is an important thing for any teacher unless they happen to be extremely experienced (ie 40 years or so of experience). As I've said before, I'm always wary of teachers who are teaching and not training.
In any case, you can get information about the larger organizations at:
Hope that helps some.