Ultimately with edged weapons, combat must have devolved into one-on-one, one-on-two, or one-on-three matches. Most of these must have been very short, although I suppose that two skilled swordsmen, equally matched, could occasionally have had extended fights, assuming their comrades did not rush in to overpower the opponent. The individual challenge matches between champions that occured occasionally throughout history probably had some of this character. A general melee or small group fight would have been different affairs. One of the tests for any warrior would have been the ability to adapt to different circumstances.
I am not a reenactor, but I do respect the ability of reenactors to generate microhistory on interesting subjects. Perhaps a couple can pitch in on this thread. One thing we don't know nearly enough about is small unit tactics on ancient and medieval battlefields. Professional warriors would presumably have learned to fight in organized teams. (They weren't stupid; they wanted to survive; and combat is an fast and effective teacher.) We just don't have enough in the written record to picture it easily. I imagine serious reenactors have rediscovered some of these lessons.
We have probably better detail about the Romans in the heydey of the legions: they were disciplined and trained, which was important; they fought in formations that allowed for mutual support; they were armored, and therefore much more willing to close with often unarmored barbarian opponents; and their training, tactics, and formations were such that they could relieve the front ranks in combat, keep fresh men to the front, and pass wounded men to the rear. It's probably an error to assume that medieval warriors were incapable of the same things, at least as far as the professionals were concerned.
We don't even really know the typical spacing of medieval forces, or the depth of formations. Pikemen presumably stood should to shoulder, but swordsmen need more room.
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!
***Professional warriors would presumably have learned to fight in organized teams. ***
I find it interesting that in Homer’s ILLIAD some of the Heros spent their time on the battlefield not fighting, but running around looking for someone worthy to fight.