The story of the bible is about mans fall and Gods plan to enable restoration back to that which was lost. Included in that is eternal life - a restoration of that intended from the beginning
I don't see much in the way of a biblical basis for your reading of the story.
IMO the story is intended as an explanation of what distinguishes humans from other animals. In a way, it is a recognition that we are animals, just like all of the others -- you could see that as consistent with evolution. However, we seem to be different, something that some people use claim that we are conscious but other animals are not. The eating of the fruit of the tree, to confer knowledge of good and evil, is the explanation for this distinction between us and other animals. The suffering of pain in childbirth is one of the costs that we are said to pay because of being conscious.