Another approach is to have your phone as the daily 2FA device and the yubikey is the backup.
Not much else you can do, the point of 2FA is that you can't get in without it.
Some services let you store multiple keys. So you can own a separate yubikey that you keep in a trusted place eg deposit box.
I could see this working for a few very secure logins, but if the idea is to two factor everything it doesn't seem tenable.
you add your main device and your backup device.
than you store the backyup device, after having it configured on your accounts, in the safe and use the main device to authenticate on a daily basis.
when you create a new account you add your main device and than when possible retrieve the backup device from storage and add the new account to it and store it back again.
on the event of you loosing your main device you retrieve the backup device from storage, use it to authenticate and remove your lost device from your accounts.
You can then acquire a new one key, add to all your accounts and store the backup in a safe again until needed.
If the site allows for UTF I register each key for that too, but only if I can also use OTP since I can't yet use UTF with my android phone.