where power is divided between a national government and the states. Election laws must be applied uniformly within a state, and all state laws must conform to federal laws and constitutional requirements.

There's a pretty good case to be made for the states having control over their elections. Local control can be preferable to central control for a variety of reasons.

The authority of the states is not absolute. Citizens of a state have recourse with the federal government if a state's election laws violate federal law.

Party politics is a whole other matter. How the political parties choose to select their candidates is largely completely up to them, although there are some aspects that are governed by both state and federal law.