Crashing into enemy formations was not a thing, because it was not survivable for the horses. Because horses are not large enough to crash through 10 or 16 ranks of infantry, their momentum works against them. Elephants could do that, but not horses. Crashing through a loose formation was possible, as was making a dense formation panic and flee.

As I mentioned, the immediate counter to a cavalry charge was feigned retreat. It worked, because it looked very much like a successful charge. You charge, the enemy breaks formation and flees. You give chase, but you are a bit too eager and proceed a bit too far. Then you find yourself in a trap, exhausted and surrounded.

You mentioned Agincourt, but the Battle of Crécy (1346) was similar but larger.