Why doesn't Sheen grant AD instead of AP?
Sheen is primarily bought by champions who, yes, frequently use spells but also rely on their basic attacks. It always feels weird for me to buy an Amplifying Tome when I don't intend to do magic damage. If you're playing traditional tank Nasus, you won't be using Spirit Fire too much. If you're Gangplank, his oranges and ult will benefit, sure, but your primary source of DPS is AD. If you're Jayce, most of your damage will be physical. Even Ezreal with his mixed values uses his basic attacks a lot. I will submit that some champs do better off with the AP, like Ekko or Fizz.
Plus, doesn't it make sense that a sword and a blue crystal make a bluish crystalline sword?
+
= 
Anyway, just a thought.
and the champs who build it? they don't plan on dealing physical damage
and
Needs the balance of AP AD and AS. take away the AP and you just have DuoForce
) especially when I'm low on mana on lb, Lich bane (which happens to also be lb) helps my autos proc and last hit champions better when everything is either unavailable or on cd
( a little)
to learn to make a stone 