Political Branding: Family and/or Party
I agree that there's definitely room for a book and/or PhD thesis about political nepotism in American history. I went to Wikipedia's lists of Governors for New Jersey and Connecticut, two states (a) I've lived in (b) that go back to the beginning. Just eyeballing the lists of names (and not doing the statistics that someone really ought to do), it seems to me that there was more nepotism before the Civil War and then again after WWII.
My preliminary hypothesis would be that the intervening period was a time when political parties were extremely strong, stronger than they are now. When party is a strong identifying brand, family or name doesn't have to be -- and may even work against one. [just spent time trying to track down the pretty good book about turn-of-the-19th-century party politics I read in the spring, failed. bah.]
Preliminary prediction: nepotistic succession will be rarer in Parliamentary systems than in the US. Prelimary test: List of recent Prime Ministers of the UK, where you have to go back to Harold Wilson to find a P.M. from a political family. By comparison with the comparable period of US Presidents, the UK PM list also comes from a wider range of class backgrounds and a *much* wider range of educational backgrounds.
Very preliminary conclusion: we need either stronger parties (fewer independents, for instance), better nepotism, or some other way for rising politicians to acquire an identifiable brand.