OP, sorry, but you are basically completely wrong. If you have a shorter 1h weapon on Horseback you are not meant to charge another enemy with a polearm.
You quite liberally use the term "completely wrong". To clarify, I am referring to attacking people on foot. The horrible attack animation often ensures your sword will sweep right above your target head instead of aiming lower. 1-H is actually pretty good in close quarter mounter combat because at least your attack animation hits at the right level.