I do know of what was once a small small frontier town in Arizona that had a local law that bars were closed on Sunday and then on election day.
Why? At the time the ONLY building big enough to host church service and election was the ONLY saloon.
That's an answer for one town.
Historically the locals say that whether or not liquor is sold on Sundays or Election Day doesn't seem to make a darn difference on either soul saving or the quality of politicians. Not then, not now.
T