During University, I was a believer in co-ops as a form of organization. I lived in and was actively involved in student housing co-ops. During grad school, I lived in a large house with 12 other people. I was the house organizer, and arranged for and paid for our internet service. Everyone else in the house gave me ~$5/mo.
Except one person, who opted out. This person was a self-described anarchist activist, and extremely active from what I could see (lots of anarchist events, protests, marches, etc.). Halfway through the year, I discovered they had just “borrowed” the password from someone else in the house almost straight away, and used the connection as much as anyone.
So the anarchist activist (who would happily give you an unsolicited lecture on how “self-organizing” works), couldn’t even self-organize with his 12 house mates, and instead let a bunch of broke students cover them. (And this person wasn’t under-privileged or anything. I’m pretty sure their education wasn’t self-funded.)
So, yeah — even if you limit an anarchist society to just the true believers, I don’t think it’s gonna work.