Depends on what you meant by "no dynasties." Do you mean, not allowing persons exercising executive power from appointing family members, close friends, etc. to other executive positions to create a sort of 'family business" model for government? If so, I think most people can get behind that and that it can be done in such a manner so as to not impede on various rights and freedoms.
If you meant not allowing the siblings, children, grandchildren, etc. of elected officials from seeking certain offices because a family member once held that office, then that's a bit more problematic.
And do you apply this outside the executive/legislative branch - ie. what about those families that generationally serve in the armed forces, or police forces? Should that be permitted? If not, how do you justify it without creating a constitutional mess?
