The most common reason is the one DisneyHorse quoted, that of not impeding the action of the shoulders. To my way of thinking that is the job of the singletree, but hey! To be fair, Hackneys and the like have such extravagant shoulder action that it would probably jerk the carriage or overtax the singletree to have them pulling from a breastcollar at full road trot. They were traditionally harnessed using neck collars in England, which neatly avoided the issue AND was ergonomic for the horse.
Sometimes the traces are wrapped because they are simply too long but often it's on purpose to minimize the flopping that results from pulling from the saddle.
Pulling from the saddle has some pretty negative consequences for the horse's comfort IMO as you have to cinch the saddle down really tightly and wrap the wrap straps as tight as they'll go to keep the shafts from slipping forward or back. In a full fine harness turnout the horse will hollow their back to allow greater movement of the front end (yes, often leaving the hind end trailing behind disconnectedly) and the horse will be checked up to maintain the overall way of moving. If a horse is built for this, it can be fine. What drives me nuts is seeing a horse who is in no way built for high action or a high headset driven that way, clearly uncomfortable but having to pull his own weight from a narrow band around his middle anyway.
I can't help but feel that asking a miniature horse to drive in that style is not the same as asking a much bigger/stronger Saddlebred or Hackney to do so as the load is proportionally much lighter for them, and I don't personally find it pleasing to the eye unless the horse is a true fine harness type in miniature and thus seems comfortable carrying himself that way. I prefer to see a horse brought along slowly and taught to use his hind end to send power up through the topline into the bridle and he can't do that if he's locking his back down to avoid a pinching saddle.
Sorry for the disconnected thoughts, I'm tired tonight.
Leia