I imagine it reduces the odds of being unhorsed too.

Yeah, you can see the rider on the right slip off his horse instead of falling off it. Falling off a horse can fuck you up if you don't know how to land or if you get a foot stuck in the stirrup but those are problems even without jousting added in. These guys probably just learn how to take a hit and how to fall in order to reduce injuries. Also a full suit of armor will stop a surprising amount of falling injuries, it's for the same reason why you wear a full suit of body armor during downhill mountain biking. Falling hurts much less with protective gear.