Since we are on a realism kick, lets keep going.
Cavalry should not be able to attack though their horses head. We all agree this is realism. We also know via realism that you cant swing a lance through a horses head.
So, to switch their attack side on a horse, cavalry riders should be required to right click to cancel any chambered attack on the right hand side before they can switch over to the left side of the horse, then they have to click the attack button to chamber again.
It's only realistic after all. Now people won't need to jump out of the way. They can just dodge to the other side of the horse away from the attack, and cavalry can no longer cheat by attacking through the horse.