Perhaps it would be more accurate to say it like this: once a minimum necessary strength is met, any extra strength does not provide an increase to damage. It's the weapon itself and the technique behind the strike that determines the effectiveness of the attack. As I stated earlier, the amount of damage from a sword strike by a trained attacker with 10 strength is going to be virtually the same as an attacker with 20 strength. They are both equally able to impale a target or sever a limb. Watch videos of people doing test cuts with swords and you'll notice that it really deosn't take a significant amount of strength to cut through an animal carcass (like a deer). It's much more about proper technique (proper draw during the cut, proper grip on the weapon, and proper cut angle to keep the blade from flexing during the cut).
It is true though, that a five year old child likely cannot cut through a deer carcass...even with proper technique. But an average strength man is going to be just as able to cut through the carcass as an NFL Linebacker...and in some instances may even be easier. The NFL Linebacker, if not practiced in proper technique, may try to rely on strength to perform the cut, and find that focusing on strength can actually be counterproductive to the attempt. And a Linebacker practiced in proper technique would find that his extra strength is wasted on the target. Like you said, a weapon can only amplify so much strength...there is a limit. To accurately model that, you'd need to list a strength modifier limit for each and every weapon. I believe that would be something that would overly complicate matters far too much.
However, the attacker with higher strength can wield bigger weapons easier, and can overcome a defenders blocks, defenses, and armor easier than someone with lesser strength.
Thus, a bonus to attacks for higher strength make sense, where a bonus to damage does not. And such a mechanic is far easier and simple, while being more realistic, than the alternatives.