In a way, that's the need Meetup.com serves, though with more of an emphasis on in-person interaction. There are quite a few Meetup groups that have grown into their own kind of social network. I suppose you could recreate these as Facebook Groups, but I think there is a need for a customizable social network platform for niche groups.
An example that come to mind is www.modelmayhem.com. It is a social network of models, photographers, makeup artists, photoshop experts, etc. It would be tough to recreate this on Facebook because you wouldn't have centralized control over photo upload approval, and you couldn't monetize membership.
If there were a platform available that let you create your own social network (and maybe there already is), it should give you the flexibility to charge for membership, give the admins control over admitting members, restricting content, access, etc. Then you can target any type of group, like teachers, tutors, and students, or the local car club, Boy Scout troops, you name it.