Your plan doesn’t sound harsh at all. Lot’s of kids are getting out of control these days and getting away with it.
The problem is that many parents use public schools as free baby sitting, and so if the school kicks the kid out the parents raise a stink. It’s often difficult for the schools to hold the line and not let them back in. In addition, if the child has a disability (which can include basic behavior issues) their hands may be tied, since they cannot kick the child out for behaving in a way caused by his *disability*. The mess is not all the fault of the schools.