Why do you think a token is required? Isn't a domain name an NFT in itself? Isn't this the logical use case for Ordinals? A means to trade and an anti-spam mechanism to limit registrations and put a cap on the resource exhaustion attack that frivolous registrations would create...
I do think that it is a little outside of the scope of Nostr protocol for this, as Nostr is a kind of pubsub peer to peer network. It is the conduit that could be used for finding registration data, but it is really a whole protocol in itself, that nip-05 could be also connected to. Just needs a short TLD to distinguish it.
Domain names simply need a way to stop a flood of registrations that result in a lot of work for the network with no compensation.
Bitcoiners need to start thinking about the question of, "ok, so, no token required, but where is this data securely and faithfully replicated to?"
IPFS? Something like IPFS? It has to have chain access if it's based on ordinal style NFTs. It needs to be possible to get paid to host the database somehow, or it needs to be essential to running an ecommerce operation so it is absorbed into the cost.