Re: “… why would use of the recovery key lock me out? … “
Good question.
Read the verbiage in this article VERY carefully (specifically the 4th complete paragraph):
Set up a recovery key for your Apple Account - Apple Support
The “Bad Day Situation” is generally a natural (or man-made) disaster where you escape w/ “only the shirt on your back” (but none of your trusted devices).
If you don’t know your Apple Account password perfectly from memory while in this incredibly stressful situation, you’ll not be able to use your Trusted Numbers, and therefore you’ll NEED your Recovery Key to regain account access.
Now, if your “Really Bad Day” disaster recovery plan has taken all this into account - with backups in strategically-dispersed AND still-accessible locations, GREAT.
If not … and you then ask Apple for help … that help will NOT be forthcoming.
Restated: When a Recovery Key is used, maintaining access to your account is ENTIRELY your responsibility. Apple generally has removed the “Safety Net”