What isn't fine is one FIDO key and no other backup. The good ones aren't fragile, but you can still easily lose them.
If there's a site you use on the phone too, newer Android devices which know how to keep a secret (e.g. a Pixel) can do WebAuthn for themselves and be that second option for you.
It does make a bit of sense. Users can't be trusted not to lose their single token. But rarely is the option to enrol a second u2f key as backup permitted.
WebAuthn (which is the one that's actually a documented standard) not only goes out of its way to make multiple tokens practical it explicitly calls out the intent that you should allow users to enrol multiple tokens.
Also, if you happen to have a Ledger for crypto crap, those support U2F as well. It's less convenient because you need to connect it to a PC, enter the PIN, and then open the U2F applet.