Your argument only holds true if you a) assume a duel or comparable situation and b) that most/all hits by both weapons are equally likely to incapacitate the opponent. The latter simply is not the case when suficient armour is used. For the time period of this mod, armour has to be graded as "almost there, but not quite yet" (as it is still mostly aimed at stopping, not deflecting blows), and, accordingly, most 2h-troops aren't the relentless grinding machines that their late medieval plate armoured, polearm-wielding counterparts would be. Still, they're often also the only professional warriors on the field, which allows them to overcome their armour deficiency unless you put them up against similarly skilled opposition (most Celtic swordsmen, despite being quite low-tier, do a good job of dealing with the 2h units).
As for "the most prized weapon was a sword" argument - well, it might have been, but not as a killing tool on a battlefield. These professional warriorswent into battle with the sword as their secondary, not their primary weapon. For that they'd use spears, or increasingly during this period, 2h axes, which became ever more viable as heavier armour became more available. Metallurgy, battlefield formations etc. also play an important role.
But then, this wasn't about realism afaik, but about a gameplay quirk that always makes Huskarls draw their secondary weapons for a charge, regardless of what you order them to use (click or alt-click).
The same goes for the useless-vs-horses argument, see the "cavalry too strong" thread for why it barely matters what you're trying to kill the cavalry with.
Edit: And to completly go off on a tangent here - re-enactments and fight reconstructions have a tendency to omit axes, maces and other weapons in favour of swords, simply because it's much harder to render them "safe" - their main targets are the head and neck, and the leverage involved means you can't really pull your punches. In a mock fight between a swordsman and an axeman, even if protective gear/armour is used, you can't really demonstrate effective axe techniques, because if you do, you will do damage to the other person. Combine that with misconceptions about swords as primary battlefield weapons, and you have a pretty solid bias against anything that isn't a sword, that you can't really overcome without inflicting serious injury. :/
Edit:2 I'm getting the feeling we're not really disagreeing here, I probably just jumped on the sword-vs-axe argument with rather too much enthusiasm... sorry about that.