Don't backup keys, rotate them.
I can't rotate my keys if I lose access to accounts because my computer died and my backup is useless.
Yeah, that's why secure enclaves embedded in complex devices are a bad idea.
Hardware keys are the way:
- Less likely to fail in the first place
- Cheap enough to have several of so you can use one to log in and manage the others in the event of loss
- Easy to move between devices
- Less likely to use the auth handshake as a side channel for things you didn't consent to