If you read about the history of the institution, this is really what was intended in its constitutional incorporation. It really wasn't about physical mail per se, and you can't hold the founders accountable to something that was outside the realm of imagination at the time.
There's all sorts of information-structural things that are in the bounds of the USPS per the intent of its creation.
I'm guessing most Americans do not realize that going back more than a decade, the USPS has scanned and stored imagery and metadata for every single piece of mail that passes through their automated sorting machines.
Look closely at the images they email you of mail coming into your mailbox and you'll notice that very often, the scans reveal the nature of the documents inside even without messing with contrast/levels.
Also, I would be concerned if all the private ISPs disappeared also. Ideally I'd like to see something like is the case with physical delivery, where you have the USPS, FexEx, UPS, DHL, etc. Having the USPS be an ISP of sorts would hopefully not kill private offerings, along the same lines. Especially so given that we're in a de facto monopoly situation at the level of specific geographic locations often now. Introducing competition where the market has failed to do so shouldn't be a problem, and if it is, there are larger issues.
If anything I could see this being selling point for private ISPs, "use us and don't worry about the government because we have everything locked down in X, Y, and Z manner."
Though an official united states citizen email address has its own pitfalls for abuse, scams, and fraud.
Many services would want to use your PKI token as identification, we would likely give up a lot of privacy because of its existence/ease-of-use.
It’s going to be an uphill battle or impossible as PKIs are too obscure for the average citizen to understand the benefits and any whiff of a federal ID card will be treated like the mark of the communist coup beast.