I'm pretty sure that you're not measuring inequality in a reasonable fashion.
Larry Ellison has a lot more resources than I do, but the net worth ratio is far greater than the opportunities ratio.
Yes, he could afford his own space program, but we both can afford to go diving. He can't drive his (much more expensive) car on 101 any faster than I can. And so on.
I'm actually running into this problem. I'm trying to get someone to help with a project. One of the sticking points is that the potential reward, while "huge" by some measures, won't significantly change what he can do. Since your model predicts otherwise, it's clearly wrong.
How about you figure out how to measure the actual "problem" before proposing solutions?