It's a US government institution, sure. Arguing about that (or focusing on it) misses the real point about how they're different from a lot of government agencies, which has everything to do with why they're acting grabby about IP like a business.
As the Wikipedia article notes, since 1971 it's been a corporation-like independent agency that's essentially unsupported by taxes. Since then it was supposed to operate in the black and it did for a long time, until it got hit by increased competition in traditional delivery services, digital communications... and the Postal Accountability and Enhancement Act of 2006 (which both keeps it from offering new "non-postal" services and gives it new obligations like prefunding healthcare obligations 75 years into the future).
I don't think treating zip or other geoinfo they've got as proprietary is a great idea, because it could be used to create a lot of value if it was let out on its own. But the value it has makes it a potential revenue source, and given the obligations and limited options they have, I can understand why they feel like they'd have to capture some of the value they've created.