In my experience, so much misbehaviour is motivated by a desire for attention. To indulge the miscreants with a sore bottom would be rewarding and endorsing their naughtiness.
Hence a much more effective means of discipline is inattention. The naughty girls can sit in detention with their panties tugged tight into their aching slits, writing lines until their wrists are sore.
Perhaps even overhearing the spanking of the Teacher’s Pet in an adjoining room. Unable to reach beneath their desks to relieve the throbbing heat, or even cease writing, the detention room being monitored by a Prefect’s remorseless gaze.
Frustration is the proper punishment for naughty girls who try to contrive their own spankings.