Almost no (current) social networks provide a service - they provide a distraction. And we're supposed to be surprised that they're having a hard time making money?
I'd say "entertainment" is a service. Although entertainment can be a distraction, it's a) not necessarily a distraction; b) a component of being entertainment. Purely (or at least mainly) being a distraction isn't a service. And it's hard to think of most "social networks" as much of anything more than a distraction.
Really, of the major social networks, I can't think of one that does anything that's not done better somewhere else. And, at least so far, no social networking site has combined those services in a synergistic way.
It's easy to make money if you're willing to set a price. The trouble for web-based distractions is that they're afraid the price will be too high and kill their traffic.
Weewar.com is a solid game, but it's still just a distraction. The way they're making money is by providing a "pro" version where you get access to more distractions: http://weewar.com/upgrade