A significant problem with 'dynasties' is that you start to get perceived, if not real conflicts of interest above and beyond governance itself.
As was pointed out in this reddit thread [1],The CEO of NPG VAN (Stu Trevelyan) is a strong supporter of Hillary Clinton and worked on the 1992 Clinton-Gore "War Room," and then in the Clinton White House [2].
Even without dynasties, its not at all uncommon (in fact, its rather routine) for either party committee chairs or firms serving parties or campaigns to have close ties to one or more of the candidates.