True, media mail is one thing that is best sent USPS, and is what I had in mind when I said "certain packages." On the other hand, if the USPS didn't exist, perhaps a shipper like UPS would offer a similar service, but since USPS already does it so cheaply (perhaps taking a loss on it and making up the difference elsewhere?), there's no point in competing in that niche.
That's the thing about the public/private argument -- as long as publicly-run entities (and USPS is one, although it's certainly more self-funded than most) are part of the competition, they distort the market, and there's no way to know how things would work if they weren't. Maybe there would be more shipping companies and types of shipping companies, and prices would come down. Or maybe certain ones would gain monopolies and prices would go up. I've seen both happen, so who knows.
I'm not saying we should be in a big hurry to kill off USPS. As government entities go, it's one of the least harmful. It mostly pays for itself, and it employs citizens who are required to put in a day's work providing an actual service to customers who can judge its quality. That makes it better than 99% of government bureaucracies, so I could easily find a thousand others to shut down first. But if it died, I don't think most people who don't work for it would miss it much.
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