What is the logic behind only using the on-deck circle closest to the dugout regardless of which side of the plate the batter is hitting from? Save time?
USA softball allows it, with the restriction that on-deck batter is behind the batter. Not aware of any other sanction that allows it. This is from 2022 USA rule 7.1:
. The on-deck batter shall take a position within the lines of the on-deck circle nearest the offensive team area. Exception: Men's Fast Pitch, Men's Modified Pitch, Women's Fast Pitch and all Junior Olympic Fast Pitch Divisions of Play may take a position within either on-deck circle as long as the on-deck batter is behind the batter and not on the batter’s open side