Why do Slows universally affect Auto Attacks?

Title^

Exhaust: Exhausts target enemy champion, slowing them by 30%, and reducing their damage dealt by 40% for 2.5 seconds. | Nowhere in this description does it say it reduces their auto attack speed, yet it slows down AA's. The same thing goes with Nasus's W or any other slowing ability in the game. I don't understand how slowing down the movement speed of an enemy, reduces the auto attack speed of a champion.

Slow's are supposed to be used to hinder the enemy movement speed, not hinder the enemies firing rate/attack rate. If their attack rate were to slow down, wouldn't that technically be tampering with time? I know this sounds crazy but think about it. Why does slowing someone from moving the legs to move, incapacitate attack speed? If it's a design flaw or if it's intentional, I have no idea. It just sounds very awkward to me and It's been on my mind for a while.