How do you handle adding both keys if you store them in different locations?
Right now I do something similar, but I have to keep a list of which accounts I need to add to key 2, and the key is offsite, so I have a several week period during which an account only has one key associated with it.
I have one key permanently plugged in to my desktop at home. I have another on my keychain that I can use at work or if I'm travelling or whatever. This allows quick access to a yubikey anywhere I am. My previous problem (when I owned only 1) was that my keys were always in another room when I was home, and getting up to get them was too annoying when logging in to things. Now I have a backup if either is lost and I'm more-or-less guaranteed to have a yubikey within reach anytime it's needed.
You may consider that the authenticator offers enough security but a Security Key is more convenient. I hate typing 6-digit codes into things, touching the little contact or pressing the button on my Security Keys is much more tolerable.
Now, personally I wouldn't want the phishable Authenticator as fallback, but it's definitely better than SMS for example.
Right now I do something similar, but I have to keep a list of which accounts I need to add to key 2, and the key is offsite, so I have a several week period during which an account only has one key associated with it.