I actually do think that in most cases it should be for-profit -- I just think that the profit can't be derived from your audience. For instance, a cafe that does online and in person orders and ALSO has an online social media hub, where people gather and interact and are also able to purchase goods from the cafe, I think would work because it's a social hub where the users are truly customers.
I think some institutions might work -- a forward-thinking library whose website isn't just an announcements and catalog site, but an actual social media hub -- but I think that'd be rare.
I don't think, by and large, private individual sites as social hubs would really work, as there's not enough draw to bring in a sufficiently large userbase to become a social hub.