My understanding is that because a loose ring bit has some “play” it encourages more chewing and mouthing of the bit, encouraging salivation, keeping the mouth more moist and sensitive. That sensitive, moist mouth, and the relaxed jaw that come from the gentle chewing and mouthing are key to the relaxation and submission we are striving for in dressage. (Chewing is good, stop strapping your horses mouths shut everyone!)
For a young horse who doesn’t have a real grasp of the aids yet, a more stable bit can be more clear, and less distracting. I don’t want my 3 year old to mouth the bit as much as I want him to turn left… turn LEFT… Please, for the love of god turn LEFT before we go through the hedge! A lot of people like a full cheek for this, and although that isn’t the REAL purpose of the full cheeks, they don’t NOT help.
Some horses, even more educated ones, just don’t like the play of a loose ring bit. Maybe they have sensitive teeth and the vibration of the rings moving against the mouthpiece annoys them, or they have sensitive lips and the sliding rings pinch. Some horses have a busier mouth and might respond really well to something with a bit more movement. Or a horse that leans on the bit might have a harder time doing so with a loose ring because it isn’t so static.
The shape of the rings can also have a big impact on how the bit sits in the mouth and across the tongue. The reason a full cheek snaffle is meant to be used with keepers is that they orient the joint up toward the roof of the mouth, and not forward toward the back of the teeth. This changes the action of the bit substantially compared to the same mouthpiece on a D ring. A baucher bit also controls how the bit is oriented in the mouth, and keeps things “quiet” and stabilized, but it also has that subtle gag action that seems to work on the lips/corners of the mouth more. Some horses love that.
Bitting is an art and science influenced by rider skill, horses mouth anatomy, discipline, trends, and above all the preferences of the horse it self. I could suppose at predisposition, but the horses would expose my ignorance. When I got my mare she was being ridden in a 3 ring gag with a waterford mouth (horrifying!). I switched her right over to a loose ring HS lozenge and I’m not entirely sure she noticed. Sorry about the book, but this stuff is interesting!