I disagree with the statements that weapons used is not important. Especially when they then go on to pick out some specific weapons types they want to distinguish!
But isn't that exactly the point - especially in a massed-battle game? The actual weapons used only matter with reference to certain units. Long spears and pikes, used in formation, should certainly be distinguished from other types. But most fantasy games have historical analogues of troops that weren't distinguishable by weapon type so much as by battlefield role: e.g. Celts, Vikings, and late-medieval foot knights.
And while those warriors may have used one-handed and two-handed weapons, they don't generally seem to have been organised into units according to weapon type. Some Thracian falxes were two-handed, but most were one-handed; I don't think there's any indication that those with two-handed variants were grouped separately on the battlefield.
Similarly, Vikings with two-handed axes don't seem to have formed specific units; indeed, the saga evidence is of warriors with highly individual preferences for weapons fighting alongside each other.
So in those contexts, distinctions like "light infantry" and "heavy infantry" or the Hordes of the Things-style "warband" and "blades" seem to make more sense than worrying about whether this unit of viking huscarls has a significantly higher proportion of Dane-axe users than that one.
I agree that you don't have to distinguish between an ordinary axe and a broadsword, say. OTOH, I think allowing a distinction between 2-handed and 1-handed weapons - sometimes grouped as "Heavy Weapons" makes sense.
Yes, I don't think we're actually that much in disagreement. In my earlier comments, I was thinking about systems like Mayhem. It's an excellent game, but the thing I like about it least is that it distinguishes between the battlefield roles of axes, blunt weapons and swords as well as "spears" and "great weapons" (which make much more sense). The game, I reckon, is much better if you ignore most of the fiddly distinctions.
I think it makes sense to distinguish two-handed weapons in some circumstances: billmen or halberdiers fighting in units of the same, for example. But in other contexts - foot knights, for example - it's the armour that matters more: those guys are going to keep coming and are going to get you, and whether they do that with a poleaxe or a sword-and-dagger combo won't matter much.
That's where I think Hordes of the Things gets it right with its balance of "quick kills" and combat ratings. So blades will usually beat warbands - but when warbands win, they'll destroy the blades rather than just push them back. That sort of thing, I think, makes for a more interesting and dramatic game than worrying about what proportion of those orcs have two-handed axes.
I also feel that the distinctions can often seem a bit ridiculous in games with different sorts of humanoid troops. Many Warhammer orcs wield one-handed weapons that are bigger and heavier than the two-handed weapons used by dwarfs and humans!
Oddly, I think
skirmish games can add a lot of interest with different weapon types, even when the effects of those weapons aren't even remotely accurate. A good example is Steve Jackson's Melee. Its strength requirements for certain weapons don't really make any sense (in real life, you don't need to be stronger to use a two-handed sword than you need to be to use a sword and shield), but they do make for an excellent game, because they force the players to make hard choices between their Strength and Dexterity stats. It really builds on the retarius vs secutor distinction that the Romans cottoned onto all those centuries ago ...
You could make the same "gameplay" argument for massed battles, I suppose, but the ebb and flow of lines and the breaking of units seems much more important there. And that's where I think the HotT approach - essentially a sophisticated sort of rock/paper/scissors - works best.