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.

The trezor one works a lot more sanely for u2f, you get a recovery key when you first set it up (it uses the screen to output it, so even if your computer has malware it can't be compromised) and can leave it in a safe at your friends place.