Mail is a low profit business, I'm not sure he'd be interested. Lot of work for nothing.
Might be low profit, but very stable.
Perhaps. The package portion, certainly, but other mail has fallen by quite a bit. That was one of the points brought up in the congressional hearing - volume has dropped 80% but the headcount hasn't changed.
The fact that USPS has to serve every person in the USA is the reason UPS and FedEx use them for last-mile delivery. Why run that many routes when someone else can do it for you and lose their money doing it. The post office is full of sunk costs - carriers have to run the route no matter the volume, and as volume drops the routes don't pay.
The constitution give government the power to establish a postal service, but it says nothing about letting someone else take it over. I suppose a broad reading says establish could also mean "appoint a carrier to do it, as long as that carrier has some federal oversight."
IANAL, YMMV, batteries not included, I'm not a doctor but I play one on TV, etc.