If you look at ALL of the notable trainers that turn out great horses from pleasure and reining western horses to high level dressage and hunt seat horses to SB or TB race horses, you will find that they all use bridles and not halters.
Some trainers, especially of really 'feely', 'light' cutting-bred horses, use side-pulls and some start by getting forward impulsion in a small round pen with no bridle, but they are cowboys that can ride a bronc if that is what the horse tries to do. Then, they quickly go to a snaffle, side-pull or bosal.
So, I personally think it is quite silly to try to invent it over. When a would-be young trainer attempts to start a horse, they are best served by using a mild 2 or 3 piece snaffle with a chin strap that prevents it going through a horse's mouth.
Remember, the person handling the reins is MUCH more important than the equipment. The best thing you can do is get someone that knows what they are doing to assist you or to actually start the horse for you. It is pretty hard to do it right when you do not know what you do not know.