heavy cavalry engaging heavy cavalry

[Domen]

are NOT classes as heavy cavalry, as they are unarmoured.

In period ca. 1550 - ca. 1770 they fought armoured and were heavy cavalry.

You are right that they evolved from light cavalry (armed with lances), but that was prior to 1550. They also eventually transformed into light cavalry - but that was after 1770 and their name was changed.

And unlike simply moving objects of mass - horses (indeed elephants and camels) have brains.

People also have brains. Actually people have much larger brains than horses.