I have a very VERY slippery dressage saddle, and my half chaps have suede on the inner leg. I find that purely for that fact they stabilize my leg because even a strong lower leg is going to struggle to stay still in a saddle as slippery as mine.
Also, they do offer a little support to the muscles, tendons and ligaments in your lower leg. For the inexperienced rider they don't do much but for the rider with a lower leg that is 'getting there but not quite there' they do help.
In jods with half chaps [do bear in mind this is a matter of different saddles as well]. Jump is 95cm according to the numbers marked on the standards. And yes, he likes to take off from WAY long, I hadn't yet figured out how to get him in deep to his fences. Now our striding is perfect 9 out of 10 times.
In jeans. No chaps. Jump is approx 1m.
BOTH ARE OLD PHOTOS, please don't crit my position! The 95cm vertical is actually an older photo, my chaps broke and then I got a new saddle and yeahhh. I've fixed my position again but don't have any recent pics. But it's more than clear that my lower leg is about a million times better in the older pic, with chaps!! Dork jumps a bit flat over the little stuff like this, once we get up to the bigger stuff [1m10 oxers and the like] he does have a lovely scopey bascule.