Well, this is just an idea, and IMHO this results in a better game-play:
Attributes determine if you can advance in a skill level or if you can gain a skill perk, so skill perks can have requirement for a minimum amount of some attributes, and advancing in skills can also have a requirement of a minimum amount of the related attributes.
Attributes can also define the minimum requirements to be able to use weapons, armors, and other items, like alembics, so you cannot use a specific sword in one-handed form unless you had for instance 50 strength, and you could not use it in two handed form unless you had 35 strength, and so on...
But attribute do not define the effectiveness of an action, so the higher skill you have in swordsmanship, or "blade", then you could use swords better, and deal more damage.
With better perks you could again deal more damage, like critical damages, head chop, or crushing blows.
With better swords, you would definitely deal more damage.
So in the end the strength attributes would affect how much damage you would deal, but indirectly as with higher strength you can advance to higher skill levels, gain higher level perks, and use better weapons.
This example can also be expanded for other attributes, and would really make action effectiveness calculation simpler, action effectiveness is dependent on skills, perks and the gear, but skills, perks and the gear depend on attributes.
Moreover raising attributes should be hard, especially in attributes that are not the main characteristics of the chosen race and class, so that individual characters would keep their individuality, and that effectively limits the skill level cap and the items that a character can use.
So if you want to finally be able to wear daedric armor and wield a daedric war hammer, then you should select a fighter-oriented race like Orc and a fighter class, it would be much easier to reach the level that you can do that, but on the other hand you would never be able to summon that devastating blizzard to wipe the scene. That would have to wait for another game and another character.
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