One key difference between USPS and UPS/Fedex is that USPS does not do freight, and they do a lot more lightweight items (i.e. letters), so cargo capacity is much less of a concern. The fact that junk mail is so common actually reduces the need for cargo capacity since their routes tend to be made long not because of physical volume/distance so much as dwell time (that is, if someone is using EDDM[0] to target a neighborhood, you have to stop at
every mailbox in that neighborhood, even if it's just to deliver that one piece of junk mail which will immediately get thrown away, and this takes far more time than delivering a bundle of packages to a handful of houses).
I remember reading about the NGDV, and one of the reasons it looks so weird is because USPS wanted a vehicle that was low to the ground (to make it easier to climb in and out of) and easy to see over the hood, even for very short drivers[1]. Given that they are in residential areas (and thus, in proximity of kids playing outside) far more often than UPS/Fedex, I can't say I disagree with that requirement. (Also, if you have a tall truck like UPS and Fedex typically roll, good luck delivering to the average mailbox while staying in your seat.)
USPS has certainly evaluated more traditional designs; in fact, they are actively using ~20k Ram ProMasters (a rebadged Fiat Ducato), which are quite similar to the Mercedes Sprinter, alongside ~9k mini vans[2].
[0]: https://www.usps.com/business/every-door-direct-mail.htm
[1]: https://x.com/Nir_Kahn/status/1364465483911675905
[2]: https://www.uspsoig.gov/sites/default/files/reports/2023-01/... (PDF page 6)