Well, not a file. A string they can copy-paste would be better, and they can share in any way they want, I would never suggest email to anyone for anything.
But maybe I don't understand how it works. What encryption? You mean encrypting their part of the key in transport so it gets to them without anyone seeing?
Also what are these assurances that Nostr provides? Nostr doesn't provide any assurances. Or are you telling me that these things that people are supposed to store for decades will just live forever in a relay that will die next month?
If all Nostr is providing is a peer-to-peer transport then I definitely do not see the benefit. Nostr could be one possible transport but why would I have to login with an nsec before I've done anything? But I was actually hoping I would just get some strings from the app and share them on Signal (just kidding, I would never trust the CIA with my strings), maybe a QR code that some stewards that are in the same room can scan from their own apps.
I was also trying to justify the Nostr to myself by the fact that it provides this bring-your-own server mechanics that allow Horcrux to work even if you die, but no, I still got to see a horcrux server URL at some point in the setup.