That sounds like the system that was in Morrowind where you had three types of damage per weapon (slash, bash, and pierce I believe). So based on how you hit someone, then there was an amount of damage done based on the weapon type. They dropped the multiple weapon stats for Oblivion but who knows if something like that might show back up in Skyrim. They have mentioned that there are perks that vary based on the weapon type, like a perk that makes mace attacks ignore armor to do more damage and a perk for axes that make the target bleed and lose health over time. So there's something to the effect of variableness to the weapon types/stats.
Morrowind had Chop, Slash and Thrust, and Oblivion sort of just force-enabled "Always Use Best Attack". Morrowind did have a range of damage for every weapon though, but I would rather see a range of damage depending on where you hit your opponent.
Yes thats is they simplified weapons too much, such additional parameters can work very well in game, problem of morrowind was not in different damage types and damage diapason, it was in chance based strikes even if player strike target in true way, thats was disappoint moment in Morrowind system.
Damage types really good was in describing properties of weapons, just need add some additional features like armor piercing for Thrust, durability damaging for Chops, bleeding for Slash, staggering for Chops, critical for Thrust, disarming for Slashes,
Axes and Maces has good chop so good for damage armor and stagger enemy, but axes has also slash so can inflict disarming and bleeding while maces good for damage armors, shields and weapons as well as for staggering enemy.
Also as well adding armor protection thats has different values for trust chop and slash.
Damage diapason can also work by describing critical chance and weapon keen
I would like seperate animations for daggers, broadswords and katanas.
Or different animations as you level up your weapon skill.
And wildly different weapon speeds based on the weight of the weapon and your strenght and stamina.
Thats it, I dont think devs will repeating they mistake in Oblivion, and weapons types will has different animations, as well there can be some unique combat movements thats achieved from perks and represent thous armor ignoring strikes, will be awesome if they are not triggered from all strikes but from certain combination of normal strikes and at end will add unique one animation, so combat will look more like fencing then button mashing.
With Perks,
Axes gives a bleeding effect, Swords will have a higher chance of critical strike and maces will ignore armor. This is just some of the perks available, so there's probably some more effects as well.
This may not be as complex as you wanted, but it's certainly moving in the right direction.
Weapons must has parameters thats represent power and chances of such values (like old Chop, Slash and Thrust), so even without perk bleeding can be done but with perk chance and magnitude will be increased significantly.