Why would I buy a two-handed sword if it still just does 1d6 damage?
Because, although you cannot wield a shield with it, it acts as a shield itself.
Why would I wear anything less than full armor class 2 as a fighting-man?
Because decreasing armor class increases encumbrance and thus slows movement.
AC, Encumbrance, MV table
We use the four M's for our combat round cycle:
If your MV rate is better than that of an opponent, you might get an extra attack during the movement phase of the round.
Formula: difference greater than 3 = success. Difference 3, opposing check on 1d6, +1 to the party with the higher rate. Equal rates, opposing check on 1d6.
But I'll throw in a bonus side affect for you: you get to be a fighting-man that looks like Conan the Barbarian.
Recall that I allow both shields and helmets to decrease AC by 1. They just can't do so cumulatively such that you would go below your class limit.
I'll even throw in something extra for you: ring mail costs and functions the same as leather. So you can wear a big ring-mail shirt, a horned helmet and wield a two-handed sword and function at armor class 5. (Or look like the above picture: no helmet but shield and regular sword. Whatever. You get the point.) You get the benefit of attack during movement phase. You are welcome.
Why can't elves wear regular armor?
Recall that, because of the nails the crucified the King of Heaven, all iron is hallowed, stopping all (non-clerical) magic.
But elves can wear bronze armor, it costs and functions the same as chainmail. Most magical armor is ancient, thus already made of bronze.
Then why couldn't magic-users wear, say, at least leather armor?
Silly. Don't you remember that, in order to cast spells, magic-users must utter the words of power and engage the somatic gestures that resonate the spell across planes? Armor would weigh down and block the somatic resonance. Everybody knows that.