On the west coast (in Seattle specifically -- but I believe the same holds true in LA or the bay area) nearly all money is new money, which forces social mobility to be tightly coupled with economic mobility.
Another significant factor is that, culturally, Americans (in my experience) more closely associate wealth with success than any other nation and success correlates directly to social value (and mobility).
While it might be possible to move up the economic rungs without moving up socially, it's not generally possible to move up the social ladder without correspondingly increasing your wealth.
(Disclaimer: I'm not by any means a member of the social elite -- to the extent that such a thing exists in Seattle -- nor am I by any means "rich")
In the UK there is a non-trivial relationship between the two.