If it's true that getting partisan politics out of the way we run elections would make elections better, then consider this from the state of Maine. The legislature there elects the Secretary of State, who serves as top elections official. Now that Democrats have taken over the legislature, they're bringing back Democrat Matthew Dunlap for another turn. From the Portland Press Herald:
Dunlap said he didn't plan to engage in politics even if it meant disappointing his party.
"I have a D after my name, so you know where I am politically on any issue you want to talk to me about," he said. "But the nature of my work cannot be partisan. It cannot be partisan. I can't emphasize that enough, especially because the work we do involves elections."
He added, "Sometimes it can be very difficult and painful and risky to say no to your friends, but you have to do it because there’s a public trust issue there. Nothing would make me happier than to leave office as a trivia question: Who was that guy?"
Dunlap owes his job to being a partisan, even as he says the work itself cannot be partisan. But that's how we run things in a lot of states now. For truly nonpartisan administration of elections, see Wisconsin.