Thanks for your comments - my goal with the writeup was to attempt to sound out why the idea of ".nonpublic" would or would not work, and I think it's clear that it's not really viable. That's a pity, as the current state of affairs isn't great. It was interesting to explore though.
Plus, you'll need cooperation from all the registrars out there that are selling domains in your .nonpublic TLD. Unless you're the only one.