I didn't say it was "the" reason it's just an example of something mandated that doesn't help their cash position. The postal service, having been mentioned even in the constitution, has a lot of such mandates that public companies don't have.

And again it's possible for something to be partially subsidized not just either income based or free. As you mentioned if it were 100% subsidized it'd lead to lots of abuse of the service. That does not mean the only alternative is it be 100% funded via shipping fees and 0% subsidized there is still 1%-99% subsidized which are valid options. Maybe you'd personally like it to not be partially subsidized but there is nothing strictly requiring it to be only one or the other.

Another example of partially subsidized services would be the roads the postal service and everyone else uses. They tend to be 30%-60% paid for by e.g. gas taxes or tolls and the rest subsidized via general taxes. That doesn't mean roads are failing to turn a profit they are also working as intended being somewhat use based and somewhat a public service.