It’s introducing one more frustrating make-work item for the human. Now I have to remember to enroll all my keys at all the sites I’ve used them for. Totally manual. Totally forgettable.
These keys should act like HSMs and have proper backup and restore. Even if it locked me into a specific key manufacturer (like lost HSM backup/restore functionality does) I’d take that over the idiotic “just have multiple keys and manage keeping them all enrolled manually” story.
Any backup is a copy.
If I lose my Nitrokey device I can buy another, initialize it with the same DKEK, and restore my key backups. (If I really want to I can decrypt my backups using my DKEK.)
If I don’t want to do any of that I can have the Nitrokey generate a random DKEK that is never exposed. Then I lose all my keys permanently when I lose the key. I have the option to choose the model that allows me to backup my keys if I want to.
If the point of the hardware key is to put the owner thru pointless make-work and risk then the hardware key is serving somebody other than the owner.
You can also add the additional keys later. If it's a serious enough account to be protecting with hardware keys, and you only have a couple keys with you, add a note in your password manager to remind you to add your other FIDO keys. You could add that note to the username so you can't login without editing the username and acknowledging it.
It sounds like a non-issue you're turning into a hypothetical concern because... I don't know, you don't like paying a quite modest amount of money for increased security?