The problem with your suggestion is that unionized paycheck leeches can’t be trusted with the proper application of corporal punishment (good teachers before you flame me think of how many co-workers fit that description). Many Principals/teachers out there will administer it with your child’s best interests in mind but there are also plenty who will administer it for petty reasons or in a vicious manner.
In todays world, where a parent cannot administer corporal punishment, in public, to an unruly child without having to worry about being reported to CPS, no government entity will administer ANY physical punishment at all without my responding to them physically.