It would be cool if instead of running some webserver to have an lnaddress, invoice requests would be a nostr note then you would only need a service listening for those notes and reply with an invoice. So a wallet would request an invoice using your npub/nip05.
Discussion
That still requires someone to run a web server, though.
Not really, you can just have a service running on your pc that listens and sends notes on Nostr, and a LN node running. I'm thinking for eg having Phoenixd on a home pc, and a mobile client that interacts with my node through Nostr send nostr command, and a service in the pc relays the commands to the node and back to the client.
But would make it easier to use an unhosted wallet.
you can get away with a wireguard connection and a reverse proxy... technically not really a web server, though it is HTTP/S
it would probably not be hard to set up a service that does this, too, paid for via LN, just nobody has, no idea why 🤷♂️
Then, the reply could be encrypted with the requestor's npub and thus private. It could all be handled by a simple "always open" Nostr client.