Well then, a quarter-cup of water can be a deadly weapon too following that absurd logic.
First and foremost to be a “deadly weapon” something must BE a weapon, it IS NOT SUFFICIENT for something to be used AS a weapon; it must be DESIGNED as a weapon.
Only then can you move on to the qualifier of ‘deadly’; working with the qualifier first as “something that COULD kill” and then expanding it to include all things which might kill which also might be used as a weapon leaves you with a truly absurd set for “deadly weapon.” {A blue whale could be deadly if dropped on someone, if dropped from a bomber as a bomb would would make it a weapon then it must be in the set... truly nonsensical.}
Contrary to your contention, the law looks at the manner in which an object (including hands or feet) is used. If that object is used in a manner that is calculated or likely to produce death or serious bodily injury, then it is a deadly weapon.
Thus, the term "deadly weapon" can be situational. For instance, if a 120 lb nerd punches a 240 lb football player in the chest, the Court is not likely to find that the fist in that case was a deadly weapon. However, if the 240 lb football player punches the 120 lb nerd in the head and then gets on top of him on the ground and then begins to pummel him in the head and face with his hands, the Court would likely find that the hands in that instance were deadly weapons.
However, in other instances, there is no situational aspect to the deadly weapon. A gun, a golf club wielded as a skull bashing device, a knife, or other like instrumentality will virtually always be considered to be a deadly weapon if used in an assaultive manner against another.
Learn the law. What you think is the law, isn't the law.