Well as long we're on the subject, I think the whole idea of naming a "successor" as you call it is pretty ridiculous. I mean sometimes when the pattern is clearly visible, I think it's fair to make comparisons like that, but there's no need to reach for them.
That really is a strange comparison. I think each of them deserves to win the Tony (though sadly I don't think Taichman will), but their styles are very different.
As for the question, I'm not really sure there is any kind of hard and fast rule.
I am a firm believer in serendipity- all the random pieces coming together in one wonderful moment, when suddenly you see what their purpose was all along.