As you rightly say, due to its architecture I don't think Nostr is ideal to replace private messaging, let alone integrate with signal.
For private messaging, p2p solutions like Berty or Keet are better, where no metadata is stored.
One thought I just had (here https://twitter.com/3d_nout/status/1615431320343044120 ).
Should people optionally associate their phone number with Nostr accounts (maybe somehow on demand encrypted)?
It would enable integration with Signal - and Signal is (afaik) superior in terms of privacy.
#[0] #[1] WDYT?
Discussion
Would it make sense to just have the number associated and when you tap on it in Nostr client, it would open Signal app? That's what I meant by integration - I don't think Signal would have to do any change here.
In this case the relays would know your phone number and any third party could collect this data.
Nostr is a decentralized protocol that is not distributed and is not intended to be private.