AP is not more effective against armor than without. It merely reduces the extra protection of the armour. I forget the exact formula, but it something like AP bonus = (Armour-3)/2.

Consider an unarmoured person - they get no benefit from armour.

An armoured person vs non-AP weapon - they get the armour stat added to their defense

An armoured person vs AP weapon - they get [Armour - AP bonus] added to their defense. This is always positive and so they are still better off than the unarmoured person.