Nerf the maneuverable horses instead.
I run around with the heavier horses every once in a while, but what people don't get it's not a rambo around and backstab lone noobs horse, it's mostly for risky infantry support.
Nerfing the arabian horse IS the first thing they should have done, 3 patches ago. And still is now. They never did it (probably the unbalance dev team did not wanted that nerf).
Maneuver, speed and low size is way more interesting than armor and charge damage. I would take a Destrier instead of my Rouncey if I could, but that leaves no gold for my armor, so I heirloomed my rouncey once and it's a bit better.
We need to take the power of agility of horses into account and balance the horse prices (decreased for armored, increased for agile). Also, because this is both more realistic and balanced, increase the riding requirement of agile horses, and decrease it for slow horses (armored ones mostly).
Devs say they want diversity on the battlefield, yet 80% of the horses I see are either coursers or arabian. The first really armored horses like chargers are the less used ones. Trolls use the PC between their naked leeching rounds, but no one uses destrier or charger.
About scores, this is true. If you are lucky you get 20 kills in a round. If not you are headshotted when you approach the enemy mob. Fighting skill won't change things much. But the ability to correctly reading the situation, supporting your melee mates and knowing when a rambo attack plan will succeed with you alive at the end, is what makes a good cavalry. In the end, your score depends on the enemy teamwork. If the enemy is blind, it's easy to pump kills without effort (those so satisfying charges when you can just randomly slash and make tons of kills, because no one noticed you). If every archer is protected, you will have an hard time killing anything.