OP didn't say it had to be free. You could also have a social network that just displayed ads without any kind of targeting and user-tracking whatsoever.
Who's to say that if the general public were presented with two free (to the user) social networks, one that targets ads and one that doesn't, that people would opt to use the targeted one over the non-targeted one?
My snarky answer is "Google vs. DDG's usage numbers," but a more serious answer is that yes, that'd be a possibility (but I'd sadly put it on the low end of probable outcomes given what we know about both the stickiness of existing social networks vs. newcomers and how much concern for privacy users actually tend to demonstrate).
Available evidence suggests that enough people want to be on whatever the biggest platform is for that to give it a decisive advantage over the competition.
