This shouldn't be a problem. Backing up a securely stored key is not a great solution. Instead you can generate a backup key that you provision everywhere as well, (the public part) but store completely offline.
Basically treat this the same as you would a physical 2fa token.
I'm thinking more about whether this could be used to store cryptocurrency keys, in place of a hardware wallet. It's a different elliptic curve (according to another HN commenter recently) but that's not necessarily a deal killer forever.
Without an export it could maybe be one key in a multisig.
Basically treat this the same as you would a physical 2fa token.