Right. The problem with the USPS is that it's both been exposed to "market competition" and also has legal obligations that its competitors do not have. The cost of those legal obligations now far outstrips the value of their statutory monopolies.
OTOH, FedEx responded to MAP-21 and similar pension funding laws by getting rid of their pension fund which I suppose isn't something USPS can do as easily. On the third hand, UPS is still able to afford pensions for union employees.
It seems that most observers agree that this is not the case, so it is unclear how you came to the exact opposite understanding. E.g. https://www.bloomberg.com/opinion/articles/2018-04-04/congre... mentions
> The law requires the Postal Service, which receives no taxpayer subsidies, to prefund its retirees' health benefits up to the year 2056. This is a $5 billion per year cost; it is a requirement that no other entity, private or public, has to make.