As matthewaveryusa says above, you can have the key on the Yubi generate then encrypt the private key; that encrypted private key is then stored on mass storage (synced to iCloud etc). Then to use it you supply the key + data to sign the auth challenge.
My issue then is that these keys allow total tracking. We need hardware implementing more complex and privacy protecting schemes (BBS+ etc).
I don't know what the Bio FIDO ones have, but if it is similar, YubiCo may not have a product well placed for a large number of RKs.
~Edit: The Bio's have the same limit of 25