Rear horse was in native as well I believe. CTRL+J sucked so it was never used. With WSE2 we can map it to whatever. I used to be in the habit of jumping whenever I was about to run a teammate over, now I'm starting to get used to pressing my "rear horse" button.
I have never seen a friendly cav do that.
It's very difficult to overcome the urge to jump instead of rear (due to having to press ctrl+j for years), but when I remember to do it, I'm thankful. Because instead of jumping down a hill, I will rear the horse and not take damage to horse, or to teammate.
Also being able to bind a key to dismount has saved me so many headaches as well. I used to always pick up items on the ground instead of dismounting.
I think you should also be able to dismount while moving (a la GTA style jumping out of moving vehicles). You should take damage depending on how fast the horse is moving, and obviously should "roll" or otherwise fall to the ground (or stumble if at really low speeds).
About "insta" stopping, your horse rears and you are stuck on the horse for a good full 2 seconds before can dismount when you rear. It's a pretty pointless act to do for any sort of offensive attack.