A couple of points to add to the discussion: writersoul, you said, “I’d just love to know what exactly was in the minds of the gedolim when they made the psak”, and, “Because it wasn’t just “ehh, let’s just asser something else for ’em.””.
I think that’s not what’s going on. There was probably never a psak on the matter, because the issue probably never came up. I would assume that the downside of having a female MK is pretty obvious, and the “upside”, egalitarianism, is not at all seen as a positive, so it seems unlikely that there was ever a female candidate suggested, and that gedolim had to pasken against it. As PAA points out, it would only happen out of great necessity, and there likely hasn’t been any; I don’t know that anyone ever “assered” it, more likely, it was never brought up. Maybe hypothetically, in the right situation (unlikely to ever happen) it would actually be deemed muttar.
The second point is on writersoul’s comment that the reason probably isn’t merely, “status quo is awesome.” Well, no, but if it came up, the idea that change without compelling reason is dangerous would surface.