So often we use stories like the story of Adam and Eve to teach moralism. The things we do are emphasized, not to show the need for a savior, but to show the need to act better. For example, because Eve disobeyed God bad things happened, so we need to obey God so good things happen to us. That's not the point of the story at all. It's never about us. It's always about Jesus and the gospel.
The reason Genesis 3 is in the Bible is to show us our need for a savior. We all inherit Adams sin, so we all need something or someone to get rid of our sin for us. Only Jesus can.