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It need to be people owned.
Sounds good on paper, but the practical implementations make them not any different than any other small service provider. cosocial.ca is a Canadian co-op for Mastodon. To become a member, you must pay CA$50 per year. What kind of “ownership” does that give to you as member? Nothing, really. You can not take control of the domain or the server.
At best, you’ll get some bureaucratic oversight and the “right” to make proposals regarding changes in governance: “use the money to upgrade the server or to pay the admin”, “Allow some members to get free access because they are facing some hardship, yes or no?” etc.
But at the end of the day, is any of that “ownership” making you (or the other members) better off compared to a service like mastodon.green, which simply charges $1/month and gives you an account?
If your idea for a good way to spend your hard-earned money is “to own” a service provider that gives you the privilege of participating in absolutely low stakes meetings, then sure, go for it. If you want, I can set up a server for you and you get in charge of finding members to join. Deal?