No. One can just remember a good password for gmail, and either use other passwords elsewhere (maybe bad, re-used, ones, or maybe good ones, not relevant if we're talking about gmail), or just always authenticate elsewhere using your gmail account.

Remembering one good password is not too onerous. Easier, it seems, that keeping any physical object in your possession if you're homeless. (I would assume that most losses are not due to cognitive failure, but instead are things like thefts when one is asleep.)