Identities are global and shared across devices. Naturally, if your keys are lost/compromised your identity is lost/compromised.

So the solution they have to this is that your real root identity delegates signing to other identities (generated local to a device) by publishing a note indicating a list of keys allowed to sign on its behalf, and presumably you keep your root identity on a trusted device (like maybe a crypto hardware wallet or a threshold multisig).

But this just reduces the problem and worsens the UX. Your identity still gets lost/compromised if the root is.

There's also an issue with how identity updates themselves work. Since these delegates are really signing for the single root, they need to be synchronized to work properly. There was a common bug (which might still happen) where if you set up your identity on a new device, the app might broadcast an identity update with an incomplete view of your identity and it resets your follows and post history. Since your identity data might be influenced based on every note you've ever sent, and message delivery is unreliable, it's hard to properly sync and reconstruct sent note history. This comes out of a fundamental design issue, where you have multiple "writers" writing to the same state. CRDTs could have helped with this, but it's too late to do that.

This sucks! It forces users to think about key management and has catastrophic failure modes. It's really hard to re-establishment trust after key compromise because there's no notion of identity that lives longer than any one key.

Matrix is not a comparable kind of protocol, but its identity management story is a lot better. Each device has a local key that never leaves the device, and when you add a new device you cross-sign it from another device you have. Homeservers maintain a list of identities tied to a user, and other people can decide to trust the device cross-signing or manually verify each of them. This can be built in a fully decentralized context (which Nostr is not, for what it's worth).