How is what you're describing different than just signing into a web-based client? Would your "public terminal" also be a relay? Something else?
Discussion
The sign-in would only be using a device. So way less friction. And maybe they’re built in such a way that they have no cache at all.
Yeah I think they’d be a relay too. Because similar to phone booths, you’d need to be able for ppl to write back to you. So maybe using that one NIP it can signal “hey I’m contacting from this relay” (or “relay network” bc the terminals would probably all be gossiped in a city at least)