This isn't to say that this is an unsolvable problem, it's not, but it's definitely worth talking about.
Post offices are geographically ubiquitous, already deal with identity verification, and already have to maintain the trustworthiness of their workforce.
I'd like to see a system where (a) an account [whether GMail, Facebook, Schwab or Bob's Online Pet Food Mart] can be tied to a real-world identity and (b) when you lose access, you can go to the local post office to verify your identity and get a one-time recovery token for a given account.
This sort of solution (and your post office idea) can be, but they don't satisfy the last resort customer service role, for people who haven't set these kinds of recovery options up.
I feel 2FA is a class libraries should be teaching. I am off to my local library to volunteer as a resource for that specific purpose. Anybody going to join me at their local library?
I was going to make the recovery code comment myself, but instead I did a search to see if anyone else had done so. Kudos. If would vote this comment to the top of the discussion if I only could. IMO it should be (part of) a PSA.
Proof of identity should be a government function, and that we likely have millions of people in the US with no way to prove their identity has real-world consequences beyond the flaw in my post-office-account-recovery-scheme; it affects access to benefits, as you said, as well as voting and being able to even prove your citizenship. That should be fixed too, but I'm not sure we can do any better for internet identity verification than the post office fallback.
Its time to bring this stupid, dystopian nightmare we’ve created to an end.
(a) still be a government agency, not a wholly-owned subsidiary,
(b) already provide email via government servers and clients in kiosks at the post office (and the personnel to staff the service and handle high-touch troubleshooting) instead of relying on private corporations and organizations to be the sole providers of what has become a necessary service, and
(c) provide basic banking services, knee-capping the payday lending and check-cashing industries.
... but it isn't that kind of country right now.
Maybe, just maybe, if people are sobbing, maybe there's a good reason why! And maybe, just maybe, if you don't want to receive such support, you can advocate for a system in which you could opt out of all such processes entirely, instead of arguing that any form of account remediation shouldn't exist.
They could preauthorize a random token amount on credit card with matching details, have you call the number on the back of your card to figure out that amount and then you have to input that number to authorize the access in an oath like flow.
Please tell me if you see something wrong with my procedure?
edit: I saw something wrong, I have forgotten about the vast unbanked population in the rest of the world as we don't have that problem in Canada¹
1) https://www.gfmag.com/global-data/economic-data/worlds-most-...
a) google will have to require a credit card in order to open an email
b) person opening an email account must actually have a line of credit, e.g.: many of the people mentioned in the OP will not have it
c) opens a new attack vector on google accounts, e.g.: people who secured their emails using 2FA app for example can now be attacked via a credit card process