Long and drawn out punishments are not beneficial for the transgressor or the victim. Corporal punishment can be administered quickly, allowing all parties to put the incident behind them and work on reconciliation and self-improvement.
In the context of a school, a drawn-out punishment process disrupts the student’s learning and wastes teachers’ time. In wider society, lengthy punishment processes are a drain on the public purse and a waste of communal resources.  Therefore, it is in everyone’s interest to adopt a punishment system that can quickly administer punishments. Corporal punishments do not require lengthy processes or jail sentences. They can be administered quickly and cheaply whenever digressions occur. 
The long term costs of corporal punishment are substantial. It leads to increased mental illness, including anxiety disorders, depression, and substance abuse. These mental health disorders take their toll on health systems and require substantial government spending. Just because corporal punishment is quick and cheap to administer, doesn't mean the effects aren't long-lasting and costly.
[P1] Punishments that are administered more quickly and cheaply are better. [P2] Corporal punishment is cheaper and quicker than other forms of punishment. [P3] Therefore, corporal punishment should be allowed.
Rejecting the premises
[Rejecting P2] The long-term costs of corporal punishment are high.