There's an adverse selection issue. Let's say you make $10/month/user from ads, and offer the option to pay $10/month to not have ads. Users with less money are less likely to take you up on that, and are also less valuable as an advertising audience, so you start bringing in much less per month per ads-only user.
Advertising effectively allows a company to charge richer users more, which you lose when you switch to a flat fee.
It seems like a chicken & egg problem, in some ways. A business that was built more traditionally than a unicorn could still make good money at $10/user/month, certainly it's possible to build Facebook-level social networking without employing nearly as many developers as they do. But without the network effect, the value is not there. I don't want to pay to be by myself.
Maybe it could work as a SaaS, selling distinct social FB-style closed social networks to families, with a future option to interconnect those.
Probably someone has already tried this and failed. I'm not an idea guy, just a coder ;-)
I view it kind of like Craigslist. If I put something there for free tons of people are interested. If I charge even a dollar the interest drops by a magnitude.
Advertising effectively allows a company to charge richer users more, which you lose when you switch to a flat fee.