A bitless bridle may be fine for some horses, but I would not trust it to work great on every horse. Some people thought/think the sidepulls were/are the most wonderful thing ever, but personally I never had any use for them. Yes, I have ridden many miles without a bit on my horses—I loved my bosal, but again, not every horse is meant to be a “hackamore horse” and there were certain horses I did not use a bosal on, because they didn’t work well in one.
The Dr. Cook bitless bridle will put some pressure around the horse’s nose, but it also puts pressure on the poll—I’ve always considered it a glorified “war bridle”—fashion a war bridle on your horse & you will get much the same effect as you get from this bitless bridle (though I know supporters of the bitless bridle do not like that comparison!!)—the bitless bridle just looks more fashionable. Put a nerve line or war bridle on a horse and he will generally become compliant, but I knew one big mare one time—she was absolutely impossible to load, so her owner put a war bridle on her-- she would hang her tongue out the side of her mouth because of the nerve pressure but she would not give in and comply with what her owner was trying to make her do. I was surprised when I saw that—I have never seen a horse resist that way! You couldn’t have paid me to put a bitless bridle on that mare & ride her—yet in a simple snaffle bit she was a wonderful ride. Same with driving—she was a safe driving horse but I would never have taken her out in the cart if she were wearing a bitless bridle instead of a bit—not after I had seen her response to a nerve line!
Driving a horse in harness puts the lines in a different location than they are in when you are riding that horse, and I simply do not see the bitless bridle as being appropriate for harness horses. I once tried to drive a Morgan gelding in the bit I usually rode him in. It did not work at all, because with the driving lines run through the terrets, the bit took on a different action than it had when I was riding the horse, and he simply did not respond well to it that way. In my view the bitless bridle is not appropriate for driving, though I know some people use it for that purpose. You will surely get away with it on some horses, but I would not consider it safe for any and every horse.