But I don't think it would work (and I'd totally work on something like this if I thought it would). People say they care about privacy, but when you present them with the option of paying $5/mo for a service that respects their privacy or using a "free" service that tracks everything they do and sells that data to anyone who'll pay, they'll almost always opt for the latter.
Now, I would certainly pay a monthly fee for a non-user-hostile social network experience. And I would consider the smaller user base a feature, so long as it wasn't too small.
FB does tens of billions in revenue on 2.1 or 2.2B users worldwide. Far more than $5 a year. I assume a $10 a year social network could break even or even profit. But how many people will really pay? Especially when you scope out to every type of person from every country FB has a hold on.
I made a $100 phone call to a girl I met on vacation in 1990.
I use FB as I attend various gatherings that organise there, but I no longer contribute much, and am phasing it out.
Considering that every other startup has wanted to build "Facebook/MySpace/Twitter BUT FOR XXXX" for the last decade, I guarantee what you want is out there (or has existed at some point), but nobody is on it and nobody has heard of it, because it costs money and nobody is going to pay money for a social network that's empty. I personally wouldn't pay money for a social network that's not empty, either... and I'm sure a lot of people share my sentiment.
An anecdote from a recent experience: I'm in India and there is the Aadhar project which assigns unique id to every citizen. There is a big privacy debate about it in the cities regarding privacy issues as the govt is forcing everyone to link our assets and tax numbers to it. People in the villages have no idea about it and there were pamphlets of Aadhar numbers being used as tissue papers in a local snack shops. But they all have a Facebook account for sure.
People don't understand understand privacy when they just want to survive.
I think they were already profitable by te time they sold out.
There's also other monetization options:
API access for businesses.
Premium accounts.
Etc.
And FTR: I'd gladly paid 10 times as much as WhatsApp charged if that was the price- as long as they didn't sell out to my enemies.