I never remove a hand cart from a loaded truck, just won't do it... and I don't like it, it isn't me.
Now, empty trucks are fair game.
My center's safety committee made it a point have a hand cart in every car & spare ones available for the customer counter. I think they ordered a couple each month till their goal was reached.
Right before I retired the UPS Freight driver was at one of my pickups & he asked me if I could sign for 2 carts and take them back to the Center. He was already 20 miles away from the center so I think i was taking care of his misloads.
You all know who got a new cart that day!