Tbh, I can't think of any animal that should be completely loose during transport in any situation. Even a dog that loves riding in a car needs at least a safety harness.

Livestock? They'll get hurt bad without restrictions on movement. They could be pets instead of food, and you'd still need them restrained during travel if you want them and the vehicle safe. But livestock that have never been (or can't be) trained the way pets are, it's exactly like you said, you want them to stay as still as possible without causing blood flow restrictions. It's safer for them, for the vehicle, and for everyone else on the road.