Make sure there aren't any tooth issues.
Horses can also have thick tongues or low palettes and can't adjust to a bit.
One of my Walking Horses is 19-1/2; I bought him when he was 2-1/2 and the Seller told me he would not wear a bit, no matter what.
I tried everything including a three ounce sweet bit but, in the end (only a few weeks later), I put a mechanical hackamore on him and he's been chugging down the trails in that hackamore his entire life.
He has a champagne-smooth running walk that I have never had to tweek. He was born gaiting like a champ and has always performed on a loose rein. Well most of the time; as with all horses, he has his moments (generally coming home) and I have to hold him back:)
He is my snottiest horse yet has never tried to run away.
I had another TWH that did famously in a Dr. Cook's bitless.
Both these horses are and were barefoot. Don't need a bit and don't need special shoes for a horse to gait properly - at least none of mine ever have:)
As with anything, these types of bridles have pressure points and require light hands. I have read of nose damage from too much jerking/pressure on a mechanical hackamore and too much poll pressure from a Dr. Cook's (or similar0 could cause damage.
Hope this helps:)