Following up on Robin's question I think the answer is yes, mostly. We are talking about the time series here, as people rise in influence. I see a few mechanisms:
1. People "sell out" to become more influential.
2. As people become more influential, they are less interested in offending their new status quo-oriented friends.
3. As people become more influential, their opinion of the status quo rises, because they see it rewarding them and thus meritorious.
4. The status quo is good at spotting interesting, unusual people who will evolve (sell out?) and elevating them to positions of influence.
5. Oddballs who are influential arrive first at where the status quo is later headed, and eventually they end up looking conventional.
6. Influential people are asked to write increasingly on general interest topics ("How to Be Nice to Dogs") and thus they find it harder to be truly unconventional. They cultivate skills of conventionality because that is what they are paid for or allowed to express.
Can you think of other mechanisms? Who are some test cases for these hypotheses?