When I’m talking about states, I’m especially referring to nation states, hence my focus on nationalists. Sure, you can use a very broad definition, but than “state” barely means anything.
Centralization is a core aspect of states, true. I don’t see how “centralized education” is so inevitable for you? Why not a decentralized education system that focuses more on voluntariness and empowering that on enforcement?
Last but not least: Building systems in not the same as sates building. And human nature isn’t as straight forward as it seems to be. You haven’t seen any other system in your life I assume, and neither have I. So it’s easy to think that’s just how it is. The great David Graeber once said in an interview that anthropologists have an affinity to anarchism since they know it works.