So to be clear, you're saying we should take all attributes away, or just strength/int/dex? Either way, interesting idea, but not sure if eliminating some of or a whole aspect of character customization would add more variety of character development. Personally, I'd prefer it if it they just made each attribute useful to all classes. This is one thing I think Pillars of Eternity did pretty well. Instead of Strength, they had Might, which increased damage globally, for example. I mean, they could keep the attributes affecting primary skills like Man-At-Arms, since a weak warrior is generally going to have some trouble, but giving Strength utility for mages, rogues, and wizards too would be cool. Strength influences carry weight and throw distance, sure, but that's not that important.
Here are some ideas:
Strength
-a global +range modifier for non-melee attacks, including for spells and bows
-knockback chance or global knockdown chance
-influences bodybuilding resists slightly
Dexterity (already somewhat universal with added dodge chance)
-Global reduction in cooldowns for all schools (very minor, but will add up)
-Knockdown resist
-Chance to resist status effects when running through surfaces
Intelligence
-Extra ability points on level up (I'm thinking a very minimal effect, but will award a few points through the game.)
-influences willpower resists slightly
-increases status application chance for all school skills.
Perception should just give a better initiative bonus and other bonuses to first turn, and I think it'd be a better attribute for everyone.
Just some ideas.