I would add to your excellent points that most medieval "infantry" were like pickup football squads -- improperly equipped, lightly trained, and to borrow a term form the gun-powder era -- "Cannon Fodder". Most of the carnage would have been an armored knight (and his skilled Men-at-Arms) plowing through groups of peasants in an attempt to get at an opposing group of armed & armored men. This is all AFTER clearing the killing zone created by your opponent's archers. Bloody stuff!
For the most part, peasants had no place in medieval armies. Fighting was for free men, not serfs.
Good points.
Another thing to remember is that most of the killing on ancient and medieval battlefields occurred in the pursuit, after a formation was broken and the losers began to flee. This is simple enough to visualize. We don’t know nearly enough, however, about the opening phases of a general engagement. What was the individual spacing on the line? How deep were the formations? What was the structure of both formal and informal combat teams and how did these units function in battle? Presumably both infantries would have tried to keep ranks. Presumably experienced warriors would have understood the need to avoid crowding. Presumably small teams, formal or informal, would have been formed for mutual protection. We just don’t know much about it.
There are hints in the literature, and some of the Roman terms have survived. The word escapes me at the moment, but the Romans had a term, for example, for small wedge formations that would attempt to penetrate an opposing line. I imagine one or two legionnaires at the point, and maybe ten or a dozen covering flanks and rear. All rehearsed and part of small unit battle doctrine, but largely lost to history. I would guess that professional soldiers in medieval armies had similar tactics.
The movies tend to show either stylized duels, which one understands as a dramatic convention, or massive, formless brawls. What is left out of the picture is the broad middle ground of well-practiced teamwork at the small group level.