Earlier quoted context omitted.
This is really awful, for it to work well you would need to buy multiple keys and each time use them all to register (which precludes the option of storing the backup key somewhere safe). Straight from the yubico website: "It is recommended that users register at least two U2F devices with every service provider should a U2F device be misplaced" That's just a plain usability nightmare, and not to mention expensive. T…
Part of the point of hardware tokens is that you can't back up and restore their keys. If backup and restore is important to your userbase, you should stick with soft tokens.
Instead, I would argue that plain-text export of private and secret keys is undesirable, as it removes any protections the HSM was supposed to provide (2 man rule for access, audit of use, etc). Back-up schemes that export these keys (in encrypted form) to another HSM that enforces the same rules as the original HSM can be useful, IMO.