For consumers, I believe that the distinction between broken vs lost/stolen is very hard to explain. Think also to a company where you deploy security devices. An employee suddenly needs a backup device. Helpdesk should investigate if it was broken, or lost. It's simply a mess.
For a possible solution, I think there should be a protocol where a user can export the key, encrypted for a backup device.
At a high level: 1) insert the backup device and start the backup process, this export a public key, proof of possession of the corresponding private key, attestation certificate 2) insert the primary device, export the key: upon validating attestation and proof of possession, encrypts the key for the backup device and export the blob, 3) re-insert the backup device to receive the key, decrypt, store and use it. Since this moment on, the device should clearly look as a backup, for example the led could be red instead of blue (see, for example, how MetaMask displays imported keys).
I don't think the protocol is really important here, I think what's really important is that: 1) the user should be the one creating the backup device, if he's knowledgeable enough and understands the risks and uses, and 2) most importantly, there shouldn't be a way to flash a security device with untrusted code.
I'd be curious to hear what people think about this, would backup be useful to you? We're working on the new gen of u2fzero (https://solokeys.com), and this could be a nice feature to add if people feel it's needed.