To veer off the topic of eugenics a little.
> We don't really know what makes someone "better", we don't know how to do it, and we don't even know how to define "better".
All of your problems go away if we use a "better" definition of "better".
What makes someone a "better" leader? That they were educated and raised in a "better" way. What makes that way "better"? Well, it should be evident - it, after all, produces "better" leaders.
True, it does lead to a kind of circular thinking, but that's allright - a lot of ink gets spilled to justify subjective preferences on objective grounds, like the ones I just described. If people can feel utterly convinced that by applying such circular criteria, they can demarcate that one piece of music is objectively better than another, surely those people would feel just as justified to use such circular criteria to decide that one leader's education, and upbringing, and social background is objectively better than another.
As long as you can let current leaders pick future leaders, you will indeed have a definition of "better". You might not like that definition very much, though.