Yeah the encryption is what protects the raw share data from the transport infrastructure. Each key (Shamir share) is gift wrapped to the intended steward's private key. The invitation link dance when inviting stewards (which does use a horcrux url, but doesn't have to) is essentially setting up an authorized set of keys so when your app sees a recovery request it's easy to discard bad actors.
So Nostr is a peer to peer transport layer but it's also the identity layer. The nostr events only need to stay on the relay long enough for the stewards to fetch the latest ones, so in most cases just a few days. And yeah I think being able to choose your own server is a big deal for something you want to last a long time. If I had used p2panda or iroh or ssb instead of Nostr I would still need a store-and-forward server.