You might find this post I made a few weeks ago useful. To expand on it, I do think there's too much distinction made between heavy and light cavalry within a western European context, and indeed between infantry and cavalry. Reality was messier than that.

Let's start with a brief primer on what John Gillingham calls Vegetian warfare. Medieval military thinkers, probably influenced by the late Roman writer Vegetius, generally tried to avoid risky pitched battles. A wholly defeated army was at best very difficult to replace, and at worst an irrecoverable catastrophe. Nor did they generally aim to wholly defeat their opponents, in the way Clausewitz would understand it. Instead, medieval rulers fought limited wars with limited forces and the goal of minimizing risk.

This meant, essentially, positional warfare, built around holding - and contesting - key fortified points which both controlled the countryside and served as bases for offensive action. In order to weaken these fortifications, medieval rulers struck at the land. When a raiding party burned and plundered, it struck its opponent twice, weakening him economically and harming his reputation. Depending on the stakes, this might be enough to resolve the conflict. When, or if, the time came to strike directly at a fortification, further plundering (euphemistically foraging) supported the army on the march, which with few exceptions was dependent on mass theft to stay in the field. In this situation, the defender would take advantage of his better logistics, keep his force concentrated, and try to drive in the foraging parties; if the invading army couldn't pillage, it had to retreat or give battle.

So, this is the small beer of medieval warfare: an awful lot of raiding and skirmishing. In this context, mounted soldiers, regardless of their skill as cavalry, had an advantage in mobility over any infantrymen. A lot of what are commonly called light cavalry were basically just mounted infantry who expected to dismount to fight. And, indeed, knights and men at arms were not averse to fighting on their own two legs. Regardless of how horsemen fought, they could get where they needed to be quicker and in better shape than walking men.

Let me reiterate that knights and later men at arms were not limited to fighting in any one particular style. They did not depend on the couched lance charge to secure victory - full stop. All indications are they took a full and active part in the "irregular" warfare that dominated in the Middle Ages. My personal opinion is that the heavy horsemen probably occupied a reserve role, standing by and waiting for an enemy force to sortie against the raid.