It is not "limiting" to make distinctions that capture real differences.  An overly broad generalization limits what can be proved.  Can we prove that every vehicle with wheels has a motor?  Of course not -- bicycles exist.  Can we prove every car has a motor?  Yes we can.  Throwing bottoms into the collection of values is like throwing bicycles into the collection of cars.  We can say /less/ about the collection than we could before, /because/ the collection is more general.