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.