From my understanding the size of your empire plays a large factor in the amount of authority you have. This would mean large empires would essentially be able to field far more heavy cavalry and therein greatly overpower their smaller neighbors, which could create obvious players for the computer controlled kingdoms.

I think the best solution would be to have one or more of the following.

-Require the armoury necessary to fashion said armor for a unit before it can be created. This would have the side-effect of also likely helping diversify field armies. A less positive side-effect may be that the Computer may not understand this new requirement and throw hordes of unarmoured/lightly armoured units around.

-Decrease the recruitment cost of knights while greatly increasing their upkeep. This would reflect how these men have come fully trained and equipped and therefore need not be paid for it to be done, and are obligated to serve in some manner. However they will demand their share of the spoils, and their equipment and mounts must be tended to, and that costs a hefty sum.

-Spearmen and pikemen in their current state are near useless at stopping a cavalry charge. Increase the spear attribute bonus to allow them to inflict greater damage vs horsemen and/or increase their attack/defense bonuses. For pikemen you may wish to do a similiar alteration, but also remove their secondary weapon (Sword) as when they dont have it to fall back on, they continue to use their pikes the way they were meant to and actually hold their ground.

-For more elite cavalry units, make their numbers per unit lower, and/or increase the number of men per spear/pike unit.