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.

Adding to that the USPS receive several billion in tax dollars every few years. It's not a consistent thing. During Covid they received $8.6B in tax dollars. A few years prior around 2015 they received $18B. In 2022 they received $50B. It happens when they go into a loss year. Their website says they are entirely self funded and I am not sure why they are permitted to say that. Maybe it's an accounting legalese thing.

I can think of a specific use-case where this could make sense if done right. If I had a USPS managed secure email account that was documented in places such as the IRS, any federal or state medical benefits and they required client keys such as GPG/PGP for communication with the IRS, ID.me contractors, DoD / Military and other agencies then it might make sense, especially if they have extra validation steps for anything purporting to be from said agencies like deep chain validation of each transport layer and relay domain with approve-listed sending servers/domains per agency and a relationship with a large anti-fraud group that relentlessly pursues anyone trying to defraud an account holder.

I think it would make sense to have a government validated email account for interactions with the government. The physical post offices should also be able to assist anyone with their issues with said account, including validating and documenting government ID's, resetting passwords and managing GPG keys.

Also, do you have any privacy concerns with a mailbox hosted by the post office?

do you have any privacy concerns

Both of those I would answer with "It depends". I envision a 2 tier system.

Tier 1: FREE, paid with tax dollars

- Restricted to sending and receiving emails to/from verified and approved government entities and to other tier-1 account holders. This tier must be explicitly protected by the First Amendment of the United States of America. This should be paid by tax dollars and the UI/UX developers should attempt to make E2EE seamless but not perfect meaning that the government could intercept this if they so desired, ideally with a warrant one would hope because this is all official government communications. So this tier's privacy and security should at least be on-par with Signal.

- This tier >must< have zero spam. It must be next to impossible to spam an account in this tier because all sending domains and relays are validated. Exception would be if someone in the government had an infected machine but that must be detected and remediate immediately and transparently, meaning their supervisor sends an email to all those affected apologizing. Tier-1 to Tier-1 should have UX options enabled by default to only permit approved Tier-1 senders i.e. family members, friends People should be able to send friend requests that would present a LOT of information about their account to the recipient to validate WHO they are.

- There should be little expectations legally of privacy on this tier and numerous warnings and disclaimers to this point. What I mean to say is, little expectation of privacy from the government, but good expectation of privacy from non US government entities.

Tier 2: Not Free

- In this tier people should be able to use their own email client anything that can do IMAPS, transport encryption enforced and they should be able to use their own encryption methods in addition to anything the USPS system provides. True privacy would be up to the account holder but they can send and receive email to/from anyone.

- Mailbox size and message size limits based on what they pay.

- When people abuse their account spam, flooding, etc... they are then restricted to the free Tier 1 so they can only communicate with the government until they work things out at the post office. If the abuse is doing something illegal then they receive a Darwin award and get perma-restricted to tier-1. Tier-1 holders must be able to access their accounts from within prison and would be a free method of communication with their family members. Laws must be put in place to ensure that it is impossible to deny access to Tier-1 to any US citizen.