This means that all relays would have to close, preventing new key pair creations that are not by invitation. How would they prevent spurious key pair generations? How would they secure existing keys? How would they segregate misbehaving relays?
This post made think that for those whose goal it is to #growNostr, which is a lot of us on the network, an invite-only system seems to attract interest in new things. It creates like an artificial scarcity and FOMO. It appears this worked well for BlueSky, and I think even Facebook and Gmail accounts did that in the beginning. Since Nostr is already out there, perhaps a new Nostr client, maybe like the one nostr:nprofile1qqsgydql3q4ka27d9wnlrmus4tvkrnc8ftc4h8h5fgyln54gl0a7dgspzemhxue69uhhyetvv9ujuurjd9kkzmpwdejhgqg5waehxw309aex2mrp0yhxgctdw4eju6t0qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyfehcpn has teased, might use that strategy and attract a lot of new users with it. Perhaps you could only login to the client or use it if some existing user has invited you (if that is technically possible with Nostr, given interoperability and all). Then you have the start of a web of trust going in and at least one other user to follow. Just a thought.
Discussion
Perhaps a client/app could be coded in such a way that you couldn't access it or use it without an invite?
I'm not a developer, though I have dabbled in software development. Just throwing out food for thought and perhaps challenges to chew on.