Hi, I drove a LLV for a couple years! It’s actually so, when they stop at a mailbox, they don’t have to leave or lean across the vehicle to reach out to a mailbox on the right side of the road. It is also easier to hop out for packages, as you said, but if I recall the volume of packages was much lower when the vehicles were designed, so they were more focused on delivering letters from one mailbox to the left.
Another fun fact, LLVs are one of the only street legal vehicles in the US with a shorter front wheel axle than the back! This makes turning much tighter so the driver can pull a full U-turn on any standard road without needing a Y-turn, since visibility is pretty awful behind the vehicle when backing up. This also makes them pretty fun to drive.
You just have to live in the right city with sufficiently high rates of alcoholism! In Fargo, ND you could get a tall 200 lb+ man proper sloshed over an evening downtown across 5-8 bars for $50 or less as recently as 2019. Not as cheap as drinking at home, but enough that most folks without kids working full-time could do it every other weekend.