Hero system (Champions/Fantasy Hero) uses DEX for attack. And defence. And speed. With the result that basically every character has high DEX.
Armour in such a system doesn't affect chance to hit, it affects damage done, and that's where strength comes in. If a defender has 5 points of armour, and gets hit by a 1d6 dagger, it only has a one in six chance of doing a single point of damage. Whereas if the attacker has enough strength to hit harder, that 1d6 becomes 2d6, and it'll get through the armour. It makes sense, although of course it does introduce more issues.