If I break my house key I can know exactly where the broken parts are but I still can't unlock my front door. "Broken" and "lost" are the same things here.
Of course you shouldn't rely solely on your phone, that's what the recovery keys any decent website makes you save or print out are for, or the other alternative 2FA options.
> If I break my house key I can know exactly where the broken parts are but I still can't unlock my front door.
This actually isn't true (it's exactly why digital 2FA is different!) If you break a physical key (already much less likely) you can still read the bitting (~ password) off of it. Bring the broken pieces to a competent locksmith and they can originate a new key for you. 2FA doesn't let you do this (intentionally, it's not a bad thing but it does mean recovery is harder).
> recovery keys any decent website makes you save or print out are for
Right, and almost all of the services that I still have on TOTP 2FA are not decently implemented... and do not have the concept of recovery keys (they are actually a somewhat recent inclusion in the setup process)! Sites that are modern enough to have made recovery codes usually also support HW tokens which I would've used instead.
Of course you shouldn't rely solely on your phone, that's what the recovery keys any decent website makes you save or print out are for, or the other alternative 2FA options.