With that being said, it strikes me there are both hard physiological and psychological factors grosso modo favouring men in combat to such a degree that their utter preponderance on the battlefield can hardly be considered surprising or attributed to societal norms primarily.
Of course, people also used to believe that there was hard evidence that "races" had different capacities for intellect, or certain types of work etc. The fact that these things are believed does not make them true.
Ceteris paribus, an advantage in strength and endurance goes a very long way, especially in hand to hand combat. Even been in a serious punchup, did boxing, jiu-jitsu etc?
Yes; Judo, Karate, and a touch of Kendo. One of the reasons I took these up is precisely because I'm a littler shorter than average. And one of the things I learned, is the the nominal advantage that a taller man might have over me can be turned into a disadvantage, because my shortness gives me a lower centre of gravity; and that can be used as a fulcrum over which that taller man can be thrown.
I've known a few women who could hold their own against average males, but they were very, very exceptional. At the higher levels of competition, this was out of the question. And I reckon this applies also for armed combat, perhaps exponentially so if large quantities of armour are involved.
And yet the reason that Danish king could not tell them apart except by their hair was precisely because they were all covered in chain.
However, aside from these mundane considerations: Since you brought up mediaeval period: Consider ie. Visby, where we do have the largest archeological post battlefield sample at least I am aware of: No evidence of females, whatsoever. Or consider an example that might be more central to the Anglo world, Hastings: Is there any indication, archeological or otherwise, that women had any role in either Guillaumes host or Harolds' Fyrd?
Absence of evidence is not evidence of absence. There is no reason to demand that this or that sample be assumed to be representative. All it is is a sample, chaotically selected. So no, I'm not aware of female skeletons found there. But I do know of skeletons found at Maiden Castle:
"The remains of 38 defenders of Maiden Castle against the attack of Vespasian and his troops in 43AD had been buried somewhat haphazardly, but with some ceremony. Of the 34 well preserved skeletons, 23 were male and 11 female. The majority were between 20 and 40 years of age and most had severe head injuries that occurred perimortem. The bones show dislocations, fractures and sword cuts, and in one case a Roman arrowhead was found still embedded in the thoracic vertebra."
- Cited as Kaslowski 1987, in Christine Quigley's Skulls And Skeletons: Human Bone Collections And Accumulations.
At any rate: I was not arguing that men and women have appeared on battlefields in anything like equal numbers. My point, rather, is that that "sprinkling" is consistent across both chronology and geography, and yet we tend to ignore it and seem to casually assume that war has only ever been a man's business. What is forgotten is that not all men are Schwarzeneggers and that not all women are dainty and delicate. Take the actress playing Brienne of Tarth in Game of Thrones; she's huge, few men would have a reach advantage over her, and I certainly wouldn't.
In the Tain Bo Cuailnge, the great hero Cuchulain is trained in combat by a woman named Scaife. And yet we skip past it, assuming it's just a bit of fantastical mythology rather than a fragment of cultural memory of real female fighters. That's what underlies constructions like kinde, kuche, kirche - not a recognition of reality, but an imposition of ideology on reality, forcing people into a stereotypical role even if that is not where their proclivities and talents lie.
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