As far as driving here in the US goes, ADS (American Driving Society) prohibits the use of bitless driving bridles & I’ve never heard of/been to a driving clinic or event where they are allowed. While the likelihood of something going wrong may be very low, if your horse does spook, it’s not just the horse that can fall on you or a stirrup to get caught up in. Parts of the carriage (especially the wheels!) can injure you worse than if a horse falls on their rider. I’ve had horses, drafts, minis, & ponies run away with me in a carriage & it can very difficult to get them stopped even with the reins in the “dead man’s slot”!
One thing I have learned, though, is that most of the horses go much better with a bit that has an arch, straight, mullen, or double-jointed mouthpiece. One mini that would completely flip out in a single-jointed half-cheek snaffle was a completely different horse when the trainer switched her to a mullen-mouth half-cheek!
"I don't ride horses just because it's fun. Ask any rider; most of them hate parts of it, but couldn’t imagine their life without it. It becomes a part of them, the love/hate relationship. It’s what we live for. It's what I live for."