You didn't answer the entire point. Don't you think we are in a much stronger PR position after we have made a visible attempt to negotiate a fair agreement? Doesn't that improve our position? To answer my own question, Of course it does.
If you are sure that our position is right and theirs is wrong what is the fear of exposing their position to daylight? We have nothing to fear from it. There is always time for war. It may look easier then diplomacy from where we stand. But then nobody is shooting at us.
If you want to analogize us as the parent in the store with the unruly child. I have always been able to outsmart kids. I usually get them to do what I want by diplomacy. Or maybe I trick them in to behaving right. But I have never had to beat or strike a child to accomplish my objective. So your analogy doesn't work for me.