I've always understood it to be the away team's choice, with some coaches not wanting to veer from the routine of a Friday night game, or the alternative, choosing Saturday and not making that long trip after a day of being in school. Especially in recent years in 3A/4A, where Lawrenceburg and East Central have been regularly running into the Gibson Southern and Memorial's of the world, those always ended up on Saturdays.
2021 Lawrenceburg at Gibson Southern still one of the best atmospheres I've seen.