They can, though, that's the point. For example, it's like the federal government charging interest on student loans, which makes zero economic sense. We have the government charging interest on its own fiat. It's a baffling and nutty policy.
This is far from a complete explanation of the logic behind charging for federal services but two examples are: 1) To restrict usage. The post office should not put U-Haul out of business because everyone starts sending their household goods through the mail. 2) Benefit added. Where the basic service is free but above and beyond that has a fee. Such as getting a printed copy of an online document or insurance on a postal package. (Well the basic service is not fee either on that one.)
Oh, I know why USPS charges fees, that wasn't my point. My point is, besides my little tangent, that USPS offering banking services is a great idea. If pay-day loan operations (legal loans sharks) go out of business, so be it. They're predatory lenders and shouldn't exist to begin with.
Personally, I think USPS has a rich history and it's worth expanding the services they offer. USPS could offer financial services to roughly 68 million Americans. They could even get into small business loans, start their own credit union, all with minimal fees. It's a tremendous opportunity in my opinion.