Some elections are for federal offices, but the states hold these elections on their own.
Constitutionally, the only federal "office" that had direct elections set up by the Framers were House elections. Elections for Electors to the Electoral College were transitory, as these were not for federal "officers" serving terms. The Senate did not have elections until 1913, but even these were state-by-state elections.
-PJ
I understand that what you describe is the current situation. That is why I was proposing an alternate approach.
I see your point about the election being a state function..
HOWEVER
I see no reason why a set of standards could be made law that a state election for a federal office must meet before the FedGov would recognize the election or the results of an election.