I agree with your suggestion. I think Post Offices, DMVs, and large reputable retailers (Walmart, Target, Cellular Phone companies, etc.) could verify our identities for a small fee and help us reset our social accounts when needed. I arrived at the same conclusion and wrote a blog post about it a few years ago:
Well, good old Yahoo Mail does that. Time and time again it tries to convince me to set up 2FA (for an account I use rarely), and time and time again I say "No" - and that's it! The library patrons would probably be very happy with that...
I distinctly remember lynching from HN security crowd when SIM cards were being unlocked and moved to new people from "trusted companies" like Verizon and AT&T.
HN demanded for such security holes to be disabled and prevented - what changed since then?
What changes is that there are different needs from different segments of the world, and we have reached a problem (authentication in general) that is truly impossible to solve with our current toolset.
For me, the larger threat is that someone impersonates me and takes everything I have. If I lost my email, it would be a nightmare but I could work around significant portions of the system. For my cousin, the larger threat is losing her email, as she has no significant assets to steal but could run into every problem in the email.
There are likely people in the middle as well, and other threat vectors. (For example: caregivers committing fraud, dementia, state actors, and 20 other we could brainstorm pretty quickly.) Perhaps the right answer is that we need 20 different services that can segment. Perhaps the problem is that some sectors aren't profitable: maybe we need a grant for emails for poor people with a circle of trust.
I don't have answers. Maybe we need a collection of people to think deeply about this problem.
What changed is that we're starting to learn about the breadth of needs by people with different lives and opportunity sets, and feel at least a desire to talk through potential solutions for a subset of people who opt into it.
If the worst thing that people could commit in this discussion is hypocrisy, I'm sure they're willing to step over that line.
Walmart may be a reputable retailer, but it is utterly disreputable in being a reliable arbiter of identity. It doesn't train its employees well, its employees are often not the brightest bolts an the box, and those that are often don't give a shit.
As for post offices, they aren't eligible because half the government is actively trying to kill them.
https://www.go350.com/posts/now-they-have-2fa-problems/