I think it can be possible, but only as a closed community of people who have all been vetted first and who, most importantly, can be can be banned for bad behaviour.
Setting up such a network might be profitabel (lots of people spend quite a bit of money networking), but it is also going to be very expensive and you are going to get a lot of negative press from people whom you didn't accept and from people who will point out that you are discriminating against certain groups because your user demographics over or underrepresents certain groups.
It is never a nice job to be the one who has to man the walls, and it is not glamorous, but no Constantinople without the Theodosian Walls.
Usenet worked fairly well when you could really only get there by knowing someone. No commercial ISPs, so if you got banned, you really could face penalties at your university (I know because I was a witness at a student trial involving doing things they shouldn't on the Internet - not Usenet specifically - and while it was in no way criminal, the students were sanctioned). And you couldn't just open up a new email account with a new provider and ISP five minutes later.
Setting up such a network might be profitabel (lots of people spend quite a bit of money networking), but it is also going to be very expensive and you are going to get a lot of negative press from people whom you didn't accept and from people who will point out that you are discriminating against certain groups because your user demographics over or underrepresents certain groups.
It is never a nice job to be the one who has to man the walls, and it is not glamorous, but no Constantinople without the Theodosian Walls.