I know cavalry was primarily used to charge into faltering formations and cause chaos amongst the ranks. This in turn leads to a rout where most of the killing happens. I also know that charges into formed pikemen or spearmen was a rarity because a horse will refuse to suicide itself into a pole arm. What about something in between though. What I want to know is how effective was mounted combat against infantry still willing to fight after a charge.
An example: Cavalry charge a rank of infantry on a flank. Infantry was able to brace but wasn’t entirely formed in time. The infantry sustains casualties and is somewhat disorganized but so is the cavalry. The cavalry has pushed far enough to be enveloped. As a member of the cavalry your lance was broken in the charge and now you have a sword and shield on horseback. You are cutoff from returning to your own lines but your infantry will break through to you soon. Enemy reinforcing infantry keep you from simply pushing through. You are stuck with enemy infantry out of formation and your fellow cavalrymen disorganized. You are NOT vastly outnumbered in your local skirmish. How effective would you be at low to no speed from your mount with a sword and shield. (This is a hypothetical, I’m not a military history expert therefore it might not be totally realistic.) If you want a time period let’s go with the 100 years war.
TLDR: When my big stick breaks and I’m stuck fighting angry infantrymen am I better off on a horse?
Side note: I know hypotheticals aren’t appreciated in this sub but it was the best way to clarify.
In response to your TLDR: greatly so. Once heavy cavalry in sufficient strength penetrate an infantry formation, even if they don't break immediately, it's basically game over. The horseman is probably better armored than you, probably better trained, probably a more enthusiastic killer, and he's raining blows down on your head and neck from seven feet in the air. In addition to physical damage done, the psychological impact is huge. Snarling, stomping, 1000-pound horses with angry professional killers on their backs are pretty terrifying. Even after armor went away and infantry started toting muskets, this remained true. As late as the Franco-Prussian war, if heavy cavalry got amongst the infantry it was bad news.
I know you specified HYW era, but I'm a Norman and Anglo-Norman guy, so I'm going to roll with that. At Hastings, the biggest issue for the Norman cavalry was breaking into the English formation. Early in the day, they made at least one frontal attack up the gentle slope of the hill, but bounced off. With the Normans retreating in disorder, impetuous Englishmen broke ranks to chase them. The horsemen rallied and rode them down in the open field. After this, the Normans began to make fake charges and feigned retreats to draw more Englishmen out of the ranks. With the English weakened by losses and exhausted from being under arrow, cavalry, and infantry attack for hours, the Norman horse penetrated their ranks with one final frontal charge and commenced the slaughter.
I'm trying to think of other instances of cavalry becoming intermixed with still-formed infantry, but I'm having difficulty. Typically, the cavalry drew off if the initial charge failed to penetrate, or the infantry broke before or immediately after impact.