As a country, we’ve decided it’s in everyone’s best interest to be able to get mail. Private enterprises cannot solve global access problems because they have no incentive to go the extra mile for the last few people the system can’t reach. (Which is why internet is so shitty in rural parts of the country.)
So why not health care as well? To me, it seems like the problem are solvable.
Having the government provide the service introduces politics to the operation of running a business. Where should post offices be located, how often should mail be delivered, what products should we offer, should prices vary according to cost to delivery, etc. These issues make the USPS what it is today - a bureaucratic behemoth that is still delivering Christmas cards from 2020.
Funny you mention bad rural Internet considering that’s a problem technology and competition is about to solve.