I like how DHH thinks about it. Make a simple product (with his own words: it is not rocket surgery) which solves problems, do it for-profit and put a price on it. After earning your salary and paying your bills you can still do rocket surgery for fun and give back to the community. Or do it also for profit promoting yourself as a professional or even your product. That's totally fine for me because in Rework he even points out that this is the part of the Basecamp marketing strategy (Out-teach your competition).
If someone brands his social network as "non-profit" only to put ads on my screen hoping for my paid op-out, that is not OK for me. I trust humans who work for real money and sometimes give back to the community but I don't trust saints.
Anyhow, we may be different and that is totally OK.
Why because VC only fund monopolies and the stock market rewards giant hoards of cash off-shore. Is it fueled by jealousy, some, but imagine if all the businesses your talking about didn't have to pay 70 cents a click to advertise and they were rotated or some other more user friendly way display ads. or if you bought enough through a marketplace to cover your own costs you didn't need to see any ads.
Non-profits aren't bound to maximize profits they just have to cover costs.
I think it would be more of a protocol than a service.
A lot of Facebook's infrastructure is about advertising and tracking. Also, if you could run some kind of P2P social network you distribute a lot of the costs.
So I disagree that the choice is between a large corporate-owned social network or no social network at all. A non-profit network is feasible, if tremendously difficult.