Homeless people aren't stupid and strong password don't have to be incredibly hard to remember. I'd rather get my accounts hacked because of password reuse than lose access to my email, forever.
There is literally nothing more important than your email. Even stuff like your bank account has secondary means of recovery, whereas if you lose access to your email you're pretty much fucked.
When your account is stolen the attacker changes your password. You lose access to your email forever and lose access to all of the services that use your email as a recovery platform.
Also... maybe getting hacked is worse, or maybe loosing access is worse, but the user should have the right to make that decision! Google can set the default, but the user knows his or her own life.
It's a terrible place to be in, but isn't nowhere as bad as being a homeless person with no access to HN and Twitter, having Google delete your account and nowhere to complain about. Because that is even worse.
If an attacker breaks in and changes your password, you already do very likely permanently lose access to your email. Account recovery from that point is a hairy process even for people who have a place to safely store important documents, let alone those who don't.
> Even stuff like your bank account has secondary means of recovery
Those rely on forms of identification that the unhoused disproportionately lack (for the same reasons that they are more prone to lose access to phone numbers). This is also among the reasons why being unhoused tends to correlate with being unbanked.
This is functionally the outcome of getting hacked, if you want any kind of decent security measures.
Any way that Google can give you access back on a password-only account is going to be rife with bad actors using social engineering to gain control of accounts. As long as that form/page exists, it is a threat vector.
What you're asking is for the password to be the only proof that someone owns an account, which means a hacker can demonstrate ownership just as much as you can.
Banks have more options for account recovery because we're willing to give them a lot more info. They can force me to come in to a branch and compare my ID to my face, or ask for my SSN, or any number of things we're not comfortable handing over to Google (especially over the web).
But by definition, the homeless have already lost a home (assuming they weren't born homeless) - and I've forgotten passwords before. So "the stupid homeless just need to memorize their password" isn't a solution.
step 1: get your account hacked
step 2: hacker changes password
step 3: lose access to your email, forever
What you've presented is not in fact a dichotomy, for any practical purposes.
Security questions are probably enough, at least for people who can’t handle 2FA.