How do you distribute power with equanimity and keep it that way? I think it's impossible with any sort of inheritance. And with legions of spoiled idiots you get an acceleration of entropy, more randomness to distribute said power from the perfect peaceful normal distribution into a power law. And then you gotta redistribute it all over again.

Yes, knowing who your child is is holding back the human race from a world of perfect equality.

I'm not sure I believe that, or even think there's a way to get there from where we are now. It's truly a bizarre idea. It's just the easiest way I can see to solve the problem as stated.