Other countries (Denmark is an example) have completely privatized physical mail delivery. All official mail is electronic. There's some nostalgia for the postman on his red bicycle (or in the USA, walking the neighborhood or driving their funny looking trucks) but are they really necessary?
Edit to add: since running post offices is explicitly a Federal power, a conversion of US Mail to being electronically based would be completely within scope. There would be no arguing over "states rights" that tends to become a logjam for any other national infrastructure or policy changes.
IMO, a better option is to switch to 3 days/week delivery, and where addresses are very spread out, require centralized boxes.
Passports, driving licenses, polling cards, draft registration, pensions, company registrations, patents, copyrights, court summons, speeding fines, inheritance, tax paperwork, census, etc etc.
It’s much simpler to perform these duties if you have a means of communication that can reliably reach every citizen.
There's all sorts of philosophical arguments as well: government services shouldn't need to turn a profit, all citizens need to be able to interact with the State and the post office provides a way to do that, mail-in voting, Post Offices can offer stuff like general delivery for those without permanent addresses, etc.
Sure, by that standard we could probably reduce to weekly or even monthly mail service. It's been suggested since at least 2008 we drop Tuesday mail service as almost nobody sends mail on Saturdays and there's no mail service on Sundays.
I haven't got a snail mail from my government for years at this point, nor did I needed to send one that way.
Mail in voting.
It doesn't need to make money or "break even." We just pay the cost in tax or postage that is needed to run the service.