Instead you typically wind up with a contractor company that can work the system and they act as a middle tier that interfaces with the production company. In the case of vehicles you could imagine a low end contractor would negotiate production fleet vehicles. A mid range contractor might build custom versions using a stock base with a different cabin/storage. The large contractor can handle the full lifecycle including the protracted support and maintenance requirements.
The difference is that a government contractor has expertise in packaging everything to meet a single customer's needs. Traditional automakers don't really do this -- they build to their own spec.
More likely reason is politics.
"Our team can work with you to develop your bid or connect you with the appropriate dealer to fulfill your needs."
If they can custom design a vehicle that saves a driver 1 second per delivery, or decrease their accident rate by 1%, that could be enough savings to pay for the vehicle and then some.
Many organizations that operate at a huge scale find it beneficial to customize their essential tool set.
That being said -- The USPS definitely does have some vehicles from traditional automakers in their fleet. My mailman drives a RAM ProMaster. https://en.wikipedia.org/wiki/Fiat_Ducato It's left-hand-drive though, so I would imagine that carriers wouldn't want to drive one on a route with mailboxes at the roadside. https://hips.hearstapps.com/hmg-prod.s3.amazonaws.com/images...
(Apparently according to https://www.whatvan.co.uk/analysis-and-comment/2016/fleet-fo... there are some modified vans by peugeot to handle "rough" terrain, but that's a far cry from a custom designed custom built vehicle).
https://en.wikipedia.org/wiki/Grumman_LLV
It's essentially a new shell thrown on top of an 80's GM SUV.
Do you have left-hand drive mail vehicles in the UK? I don't recall ever seeing images of a Royal Mail delivering to a post-mounted mail box from a truck now that I think about it....
From wikipedia, Oshkosh seems be a company doing custom/specialized vehicles for all kinds of purposes, including military designs. Why does that seem like a "crazy" choice suddenly?
Anyway, I think the biggest issue is that USPS is not requiring for next gen platform to be fully electric.
It seems government contracting with a middle-man who contracts with others is how government likes it. Probably politicians are getting more influence this way, at our cost.