The issue is that even the GAO thinks there are "pyramid" issues -- the USPS revenue is going to be in a long-term decline, and peak-retirees will hit in a period where the revenue is lower than today. So, pre-funding makes a lot of sense.
Similarly, SS (and I think medicare?) were supposed to be pre-funded during high tax years of the baby boomers. There's technically a surplus, but it's invested in US treasury debt, essentially an accounting trick. (although I don't know what an SS surplus would otherwise be invested in -- you don't really want the government investing in private securities, either).
Parcel drop-off could be automated, extended hours, partnerships with businesses, etc., although I think most parcels originate from businesses now.
Maybe a good compromise would be fewer post offices, open later, and less delivery, but with mail available for pickup at the post office up to the day before delivery. This would be capital expensive vs. operating expense intensive, which should be good for the USPS (they can borrow at cheap rates, and the government could fund some of this).
