You lose out on the network effect with this solution.
If someone gets to pick who's allowed onto a network, then they won't bother using it. Maybe your friends will join since they are allowed to add _their_ friends, but those friends of friends wouldn't bother because most of their friends can't join, meaning your friends won't bother either unless they really want to talk to you specifically.
It would work for groups where most people know each other, but there are already options for that that allow users to be in groups that aren't all owned by the same person e.g. Discord, Signal, Facebook.
A total user base of 50 or so would be fine. The trick is to find a group where everyone (mostly) wants to interact. An extended family could probably work.
If someone gets to pick who's allowed onto a network, then they won't bother using it. Maybe your friends will join since they are allowed to add _their_ friends, but those friends of friends wouldn't bother because most of their friends can't join, meaning your friends won't bother either unless they really want to talk to you specifically.
It would work for groups where most people know each other, but there are already options for that that allow users to be in groups that aren't all owned by the same person e.g. Discord, Signal, Facebook.