Setting aside your utopian strawman, if your argument is going to based on historical timelines starting with when "we were kicked out of Eden", I suspect we're not going to find much common ground on history, philosophy, or morals anyway.
The original question was, what should we leave behind to future. I think ultimately it's a great question, and a great debate. Let's agree to disagree on our approaches to it.
If (a) then you are a Utopian who believes that evil is to be blamed on history or society and not men themselves. If (b) then it seems you are a fatalist who believes that there is no hope for the hypothetical survivors anyway. I don't think (b) is the case because you now mention that you have an "approach" to the problem. It is clear that we disagree on our "approaches", but what is your approach? If you believe (a), then it seems the wisest approach would be to try to keep the surviving children untainted by words or thoughts from adults who remember the cataclysm, in hopes that the new generation will start from scratch. Am I wrong?
My point is that we don't know which part is useful and which part isn't, and to presume otherwise -- ie to believe that we can effectively, if you will, "play God" with some future society after we've blown this one up -- is hubris (not to mention likely contraindicated in the Bible somewhere).