The problem is that ALL those methodologies are wrong. In order to get the most out of a draft animal you have to hook them up to conform to their body type.I don't know what you mean...They are hooked in a free way but not too bad...Would you have prefer they are hooked in other more efficient way?
Horses do not actually "pull" a wagon they push it. Their body strength is front to back and thus the design of both the harness and the wagon is designed to translate their power effectively that's why they (and cattle) are hitched the way they are.
Humans are designed to also push and not pull but because we are bipeds we need to have a solid structure in front of us (like a bar) to translate our strength into "draft". Having a girl pull a mini\pony cart as depicted here works because there is relatively little weight in it.
Moving anything over say 200 pounds and distance requires the proper harness and hitch set up.