Great, you've considered the case of N ~= 100. Don't need a state to manage that.
How about N ~= 1,000,000,000?
Anarchism (and any fully decentralized protocol) "works" for small N because the average node can keep all the other nodes of the society in memory. If you need something, you know exactly whom to ask. And if you do something wrong, everyone will remember and hold you accountable. This plainly doesn't work with millions of nodes. Same principle why Bitcoin will never take off without hacking on traditional centralized finance mechanisms like Lightning; at some N, the resources required for individual nodes to maintain an accurate representation of the entire network becomes impractical (either impossible or just way too slow).