It had very little to do with stirrups.
If Medieval cavalry ever faced infantry in disciplined close order, and charged them head on, even the Medieval cavalry would have failed. Stirrups or no stirrups. Medieval knights were successful in such charges because they mostly faced looser formations, often largely comprised of levies, that were too loosely formed to withstand them and/or broke.
Against a disciplined close order heavy infantry unit in dense shieldwall, the knights, if charging head on, would have failed (as indeed happened at Hastings against the shieldwall of the Anglo-Saxons). It was true at Hastings as it was true in the days of Ancient Greece and Rome: the disciplined Infantryman, In tight close order and densely deployed, will, if they hold, defeat cavalry when attacked head on. The cavalry just will not charge headlong in, it's suicide.
Cavalry rely on the infantry breaking. If they don't the charge must be pulled up or they risk being destroyed. (Hollywood is nonsense). Even in the days of the Napoleonics this was true.
Cavalry are for infantry in loose formation, or units that are broken or look to be about to be. They are for the flanks and for the pursuit. They are not for charging close order heavy infantry head to head and ploughing in.
I think weapons such as the 10ft Kontos were developed in order to allow cavalry to still engage close order infantry without having to plough in. Charge, pull to the side, thrust with weapon at range of six feet, then pull away again before infantry respond. Rinse and repeat. Just my thought.