Now for a more facetious response:
You have to have intelligence to beat cavalry, but cavalry can just wait until you're occupied and attack you without opposition. Yeah, guys, be intelligent! Take responsibility and change your class to succeed! In other words, roll cav.
That's what I did. Respeccing my level 33 pure shielder into a 1h/polearm hybrid for anti-cav was my way of adapting to cav as my counter. As I leveled back up, I became a cav myself. I think cav should just pay more dearly for mistakes (running into objects, getting reared, charging into too many people, etc.)
-speed based damage on collisions
-speed based damage when dehorsed (average speed would be ~20%)
-stun when horse is reared so you can't get off or stab the polearm player
-give old lance angles for spears 150 length and less. More of an anti-cav role
-More damage to head, remove extra damage to legs. Removes massive damage from teamhits to horse. Makes it difficult to charge ranged characters.
-Make it more difficult to U-turn at high speeds
(not sure about these one)
-bump damage affected less by armor. Lower bump damage for low armor, slightly higher bump damage for high armor. I wear heavy armor and can barely feel bumps, while low armored people lose half their health.
-Shield helps mitigate bump damage/higher speeds before knockdown. Was thinking to leave shielder lacking offensive capabilities against lancers, but at least receiving a few defensive ones. It would help protect low armor shielders from cav, although cav would still counter them.
-Rearing polearms do extra damage to horses. Not sure about this, but many of the support polearms can't do too much after finally stopping the horse. Sometimes they do to little damage to even kill the horse or damage the rider much.
I think increasing other class options/quirks against lancer cav would make it more skill-based. Not letting cav get away with mistakes easily would also make it more skill-based. Good ranged will be able to take out cav if they can land a headshot. Cav can avoid getting hit in the head, and would need to watch out for spear users with the wider lance angle. They would need to go a bit faster to knockdown turtles, etc. I think it would be difficult to vastly change the controls and receive a positive response and have the problems fixed.