We already have that structure. It's called "court". And if you think it's not working well, I would agree with you. But neither will the other bureaucracy you are proposing, because neither really care about any of low income people who can't even pay for the phone service.

But let's put aside the efficacy of said institution, and presume it's working very well. They got call from some Joe. He claims that certain email address belongs to him, but can't prove it. Forgot password, no access to phone. What this customer service of yours going to do? Let's imagine they can order Google to give the guy access to account. Is that a right thing to do? What if that email belongs to a journalist or a whistleblower and you just gave access to it to a Russian intelligence? Remember, benefits are one thing, but it's not the only thing for which email is used.

And if it really comes down to this, why is Google under obligation to provide emails for government use? Government can provide email access to everyone who needs it. If they require email in order to access benefits, well go ahead and set up necessary infrastructure. Why Google had to do it? Google provides service on as-is basis. If that service level is unacceptable for government use, well newsflash: it's not the only provider.

It's not the only provider, except when it is.

If you have an Android phone, your e-mail is on Gmail. It doesn't need to be, but it is, because you didn't know that when you were funnelled into the e-mail when you set up the account and oops now that you're locked out ten years later it's too late to make a choice.

Since opening all these offices costs money, this means that the accounts can't be free anymore.

I suppose they could be subsidized by the state for low income people.

That's why I proposed linking to existing services: Google doesn't want to open an office in Podunk, but they could very plausibly setup a way to allow agencies like DMVs, libraries, maybe the VA or post office, notaries, etc. to use some kind of “I attest that person X showed me photo ID matching the information on account Y” web app. This could be really useful paired with things like senior centers whose residents are far more likely to need help.

Not necessarily. The margin is really high on Google services even though they are free.

I don’t know Google well enough to know what they would need to do to offer non-shitty service. Maybe they show more ads.

I also think they could automate good service if they wanted to, but it’s not a priority and they aren’t required. I used financial services before and after CFPB and I don’t remember price increases on my bank accounts. So perhaps something similar would apply here.

Could it not be similar to FOSS companies where the software (service) is free but customers pay for support?

I write software at a fintech, and the CFPB regulations are super important for protecting the customer. They also give important guidance on how the customer needs to be taken care of, which is important for a company that wants to do the right thing but doesn't have expertise in customer service.