My local postal service used to make delivery on bicycles but they have gradually introduced golf-cart like miniature EVs. This allow each run to cover a much larger area but probably would not for the most of US because their mail routes are too long.
Also it sounds like the new trucks have pretty stringent visibility requirements, which would help avoid running over playing children in a suburban setting. I can see that as a pretty serious risk for the USPS, given how frequently they stop for a few minutes. An off-the-shelf van without the unusually shaped front probably has more blind spots a kid could sneak into.
Oshkosh is also a very well established manufacturer of vehicles for the government and holds substantial military contracts for custom vehicles such as the highly recognizable HEMTT. So the Oshkosh purchase is fairly low-risk in that Oshkosh has a proven track record of delivering vehicles for government fleets.
UPS and FedEx also make use of largely custom vehicles. They are based on off-the-shelf step vans, but to a large extent OTS step vans no longer exist in the US and nearly all of them you see are contract designs for fleets. There's a bit of a cyclical relationship here as the modern step van is basically defined by UPS and FedEx, which purchase their trucks custom to specification from body-makers like Utilimaster and formerly Grumman-Olson. Grumman popping up here again is not coincidental - the USPS and UPS formerly got their custom trucks from the same manufacturer, but Grumman-Olson is no longer nearly as important of a player as it once was.
The short answer: USPS is contracting for at least 50,000 vehicles. When you buy 50,000 of just about anything you gain a lot of leverage to customize.
Just because those things are spec'd as they are, that doesn't mean they need to be.