Maybe some amount of messaging connectivity, for a narrow set of cases like court summons and other official messages, could be run as a public service at the taxpayers' expense. But likely the bulk of it should be run as a paid service, either regular businesses, or/and non-profits that still are expected to break even.
Comparing today to 40 years ago: as far as I can tell, letter mail is virtually always used for the purpose of transacting business these days. Forty years ago, it was used for business and personal purposes. If I wanted to communicate with family on the other side of the country, it was more likely than not done by mail. Even 25 years ago, a long distance call took some thought because it was charged by the minute. These days, at least in Canada, all but the cheapest of mobile plans comes with nation wide long distance and we have the Internet. Both services are available for less than basic phone service back then.
Parcels are a different story. I can't guess how people's personal habits have changed, but the business front is very different as far as I can tell. Mail order was the exception in urban areas back then. It would have been different in rural areas, but in my explorations of the country I discovered that some towns were places where people lived while other towns were regional hubs for businesses. There would have been some mail order and a lot of doing without, but I suspect it has seen a shift where proportionally more parcels are commercial in nature. On top of that, the standards for delivery have changed. When I was a kid, it could take weeks to receive something via the postal service (from across the country). Now shipping times are more aligned with couriers.
I realize there are economic benefits to subsidized mail, but I'm not sure that subsidizing businesses should be a priority.