Close-combat cavalry is next to impotent when faced with a solid, unwavering wall of infantry in close order. (There *are* ways to get horses to charge even such, but AFAIK they're anything but reliable and don't seem to have worked too often. Although I'm under the impression some of the later cataphract types got around that by *walking* their horses into contact and simply slowly hacking their way into the ranks by the virtue of brute superior mass and armour...) Which is why it has always by preference attacked weakened and/or wavering formations, unformed flanks and rears instead, where the quirks of horse psychology don't get in the way of driving the momentum home.

The usual "division of labour" was really to have foot engage foot and horse engage horse, and the victorious cavalrymen then hopefully remembering to reform and come back to attack the preoccupied enemy infantry in the flank thus precipitating a wholesale rout. The "Alexandrian" tactical system, with pikemen holding the center line and heavy strike cavalry delivering the decisive blow on either flank (the other wing was usually left to lighter cavalry with orders to keep on the defensive and keep enemy horsemen from turning the flanks of the pikemen), is really a pretty purebred example.