Nearly everyone seems to be in agreement that Speed and Agility existing simultaneously is incredibly redundant.
I disagree. We the player might try to play smart, simply because of the fact that we don't want to die horribly repeatedly in the game. Representing their Intelligence in dialogue is vital,, however, and something that New Vegas actually managed to achieve to a great effect. I want my characters intelligence/lack thereof represented, as opposed to not having the option of responding to something they might actually have knowledge on, pointing out the flaws in somebodies logic, so and so forth. Even if the player plays smart, that doesn't mean that the character shouldn't have the option of getting the benefits of us doing so either. You could easily tie intelligence off in Melee by having it modify the amount of damage a critical hit does, or applying bonuses when attacking an enemy that has a weakness to a certain element. We can have that kind of synergy and have it represented, allowing for a more cohesive and natural attribute be properly reflected in the game.
We know you can be a thoroughly dull wizard and still be a powerful spell caster, so its not like Intelligence is vital to learning Spellcraft either. An idiot that is really good in the School of Destruction is going to be able to learn the Spells relaveant to their Skill level, no problem. But a smart character would be able to learn those spells earlier, even if their Skill isn't up to snuff. The spell might not work properly, or might consume a inordinate amount of magicka just to cast it, but they would still be able to get a graps of its concepts.
Add to it the ability to stagger (enemies that aren't undead or in heavy armor should damn well be flinching from taking an attack) and resist being staggered when attacking/being attacked, the ability to break an enemies block, and having your own block broken (whether its a physical shield or a protective ward), and not having your Spells interrupted when attacked, and I'd be sold.
Needs also how well your character can resist the chance of being crippled by an enemy attack, whether its someone trying to apply a bleed or straight shattering your bones. I'd also let Skills govern the efficiency your Stamina usage. A high Endurance might let you fight much longer, but a skilled character is going to know what are and aren't wasted movements that take up more energy then what's needed.
I'd move this out of magicka...well, most magicka related things out of everything but Willpower for the most part. Again, you can be pretty dim to be a mage in Tamriel, and an Intelligent mage would know more about magicka efficiency then merely being perceptive. Instead I'd focus on how well your character notices things in conversation and the environment, while in combat increases their Crit chance. Also, I'd like to tie how far it is when undiscovered locations on your compass appear. A character that is aware of their surroundings is going to actively pick up on more things then characters who aren't, after all.
Not a fan of a whole lot here. Honestly I'd let Stamina regeneration back be with Endurance for the most part, but...there ideally would be plenty of different ways to regenerate Stamina, especially via perks. I'm actually more okay with letting our starting regen rates for magicka and stamina remain mostly the same, with it starting to differ when our character learns new things.
Again, I'd rather avoid monotyping the Attributes to make them useful to all potential builds. Sure, high strength and endurance might be preferable to a warrior, given its nature, but ideally, I'd want all types of builds to look at an Attribute and thinking "That could be really useful for what I'm playing." Agility is a good place to start with that. Sprinting speed and general movement abilities like dodging seem ideal for rogueish characters, but things like lowering the enemies chance of landing critical blows, how quickly our character can act after being interrupted from an attack, the speed of which our character can preform the moves necessary to preform a large spell, are things all characters can benefit from.
Resisting nasty things like diseases and wounds are things that should be left to Endurance. However, Willpower affects how our character responds to them. If striken with a nasty disease, dying of hunger or thirst, or a going through a lack of sleep, a willful character is not going to be as bothered by it as others might, meaning they would see less drastic debuffs applied to them. This more suits the mental aspect Willpower over Endurance, which is more of a physical measure of how far they can push themselves before suffering the consequences. How badly they let those consequences affect them however is where the real test begins, and Willpower lets them push on regardless. This gives more physical characters a better reason to invest in this Attribute, since being able to push yourself passed ordinary limits can be a significant boon.
As I said previously, Willpower is really the only Attribute that is intrinsically tied to spellcraft and magicka in TES. As I see it, it should effect your raw Magicka primarily before everything else, with Intelligence acting as a modifier to how costly Spells could be. Also, it could be a means to how well you can Turn other creatures, resist an enemies attempts to debuff you through magic, or how an enemy resist your own Illusion spells, or how easy it is to dispel an enemies attack.
Getting into Personality, there's nothing I have a problem with there since its not hard to really deal with. Personally though, I'd like it if Strength affected Intimidation attempts, or having a low Personality actually makes it easier to do so. If you seem like a friendly sort and everyone in town knows it, it'd be harder to intimidate people because of your reputation. If your a misanthrope that everyone whispers in hushed tones about...its less so, since no one knows how you might respond.