I totally support this idea. While Constitution, Memory and Wit are already more generic attributes, I think the others indeed just limit one to a specific class, which does not go well with the otherwise open skill system.

Maybe strenght should be renamed to "force" or something if it also increases magic damage, but those are details.

One problem might however be items and armor. If there are no specific attributes for archers/melee fighters, what stops a mage from wearing heavy armor as well?
Maybe we could solve this issue by giving fitting free spells/abilities to the armor, or giving specific boni like magic dmg to cloth armour.