Yes this happens sometimes, especially when more families sent Christmas packages and mail order was king before the internet split parcel delivery among many parcel services. (When I started, FedEx was still up and coming.) In the early and mid-1980s, UPS truck availability was limited. UPS would rent U-Haul trucks to get the packages out on time. It was a love-hate relationship with those trucks.
First, there were no shelves to keep packages from sliding or to put them in sequence for delivery. Imagine moving everything in your garage to one corner, and then needing a pair of pliers. Not fun.
The trick is to load as many packages as possible on the passenger side, deliver them, and then sort again. I hated doing this because it was a time sink — most of the day was spent shifting and sorting packages rather than delivering them. Getting them all there during business hours during holidays made it more difficult. However, the good part of driving a U-Haul truck was its automatic transmission, air-conditioner/heater, and AM/FM radio — three amenities that were never available in UPS's brown trucks.