W.r.t yubico u2f you don't backup it you just register to or more tokens that work as backup keys.
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.
I'm not saying soft tokens are bad. They're not; they're great. When we get a workable U2F software token, that might be the best option for most people.
What I'm saying is don't spend money on a hardware solution that isn't buying you any meaningful additional security.
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.
My point is not that backup and restore is intrinsically evil; it's a legit security/usability tradeoff. I think most people should use software tokens.