Many times I read on HN that people are tired of having their email scraped for advertising by Google and Yahoo, but the pain of standing up your own and domain and mail exchange is so high that many don't bother to move.
If the USPS offered every American a free email box -- universal email service, essentially -- would you take them up on the offer? Are there any limits (e.g. attachment size or retention) that would make you say no? Or are there services (e.g. certified email or digital stamps to reduce spam) that might make you say yes?
Keep in mind that this would be universal email access, so it has to be simple enough to be universal; this would probably preclude many customization options like "bring you own domain".
USPS is technically incompetent. Like, wow. They're remarkably good at keeping decades-old trucks running and at deciphering handwritten, mis-addressed labels, but that's because they've kept people with those skills on staff ... and nearly nobody else.
USPS is already becoming an advertising company. "Marketing mail" is over 20% of revenue (FY 2022), but that doesn't include targeted (first class) ads nor resale (eg periodicals). And with the consistent push to "run it like a private business" (despite having both products and services effectively set by law), I can't see why they wouldn't scrape their email to generate revenue.
There are many options between the extremes of ad-supported and self-hosting. The private sector fills that need, so the government need not step in.
There are people who think public transit should be free but others think that you're better off paying for it if it means there is more funding for a quality service. The last thing I'd want is a "free" service that sucks, I'd much rather pay for a quality service like Fastmail.