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I assume by webbing you are referring to a nylon harness. (If I'm wrong, just ignore this post.)
Most nylon harnesses are far from ideal, but we do have one that is mostly synthetic (saddle, blinders, girth, crupper, breast collar, padding are synthetic, strapping is nylon) that works well. It actually fits and has wired blinder stays, both of which are rare for a nylon harness. Many (if not most) are notorious for poor fit, little padding, and no structure. These are VERY uncomfortable for the horse, especially if the nylon stiffens with age, dirt and weather. Keep in mind that in the event of an accident, nylon won't break, creating a potentially dangerous situation. Also beware of cheap buckles that could break and cause a wreck.
I have read that fabric softener works to soften up the nylon, but I don't know what it does to the durability.
If you are certain that the rest of your harness is comfortable, you might consider upgrading the bridle. Just be sure to place your horse's comfort first so that he can enjoy driving.