Well there have been studies that show humans are naturally more risk averse and that they try to minimize losses over risking for an advantage even when the odds are exactly the same. I don't really believe that most people would take some sort of gamble about ending up in the top or the middle.
Yes, there are many studies on this, and one thing they definitely show is that there are a lot more factors that play into the decision than simply a rational analysis of the facts. That's where the idea breaks down.
As I said in my initial post, I think certain people are just unwilling to imagine being born into a disadvantaged situation. You've just tried to rationalize your way out of doing that here.
Nonsense. I'm fully capable of understanding that I could be anywhere in the spectrum of success in this fictional setup, but that doesn't mean I would design the world based on that possibility. I would not. And given thousands of years of evidence around us, neither would anyone else.