But elections also serve as a bright line to settle an issue. We could argue forever about who "really" has the most votes, but eventually we have to say who won, and elections are just as much about finality on that issue as they are as an evidential test of fact.

To an extent, then, it doesn't matter that Greene didn't "really" get the most votes. If you allow every election to be indefinitely contested until you're convinced there's no reason the loser really should have won, elections never settle anything.

Yes. Exactly. This is true for lawsuits as well: getting a final answer is more important than getting the "right" answer, which is why finality is an important judicial value that courts balance.