Google will lock you out of an account even if you remember your password. This happened to me, when Google decided to use the recovery email address for 2FA, locking me out of my primary account. And the exact same change was made to my recovery account, at the same time. As for the recovery email of my recovery emails address, it was with a company that hadn't existed for over a decade, and no longer existed.

As long as the automated flow works everything is great. But if the music stops can you get in touch with a human to fix it? That applies not just to auth but pretty much all of their stuff. Plenty of horror stories have made it to the HN front page over the years.