Quick online search suggests it’s for pedestrian safety and preventing damage which makes sense, mail trucks are driving super close to stuff all the time
They are probably not putting one of the most expensive and unrepairable components in the bumper. The bumpers look ugly because they aren't integrated into the car body/metawork, and can be more easily replaced.
I do wonder if bumpers that low will have mismatch problems with higher modern cars (aka SUVs and trucks), whose bumpers may go right over the mail trucks' bumpers and cause major damage.
I wouldn't think you'd do it full length to the front, just closer to behind the dash where you could get some extra battery in but still have lots of crumple zone in front of it.
Just a guess. I'd love to see a video giving a deep overview of these the way you see car reviews on YouTube.