You touch on a couple of interesting points, Buka. First, I agree with you regarding "zero tolerance" policies. While I believe they were originally coming from a good place (a strong, principled stand against violence in the schools), they are often a way for schools to avoid taking responsibility for 1: exercising sound judgment within the context of the specific events and 2: advocate for the kids who are involved.
They do also typically end up inviting police involvement to a sometimes ridiculous degree.
Schools should, in my opinion, have clear, reasonable policies in place to address issues. These policies should afford the school the latitude to exercise sound judgment. There should also be a way for parents to appeal any adverse actions taken by the school.
The other, balancing side of this is that all of the kids, yes, even the bullies, have a right to education. While not a guaranteed right under the US Constitution (although it should be, IMO), most State constitutions guarantee this right, and those States which don't still recognize the need to provide a foundational education. Add to this that many bullies, most bullies, grow up to be decent human beings, and anything more than a short term suspension can significantly change the trajectory of a child's life (particularly if school is that child's only real relief from a difficult life outside of school).
Point is, I agree with you, but with the caveat that any discussion that involves kids needs to consider the welfare of ALL of the kids, which includes the bullies, in my opinion. All kids are incomplete human beings, in my opinion. They're all learning to be happy, healthy and productive adults.
Ultimately, we already have too many non-criminals in prison. A bunch of pot smoking hippies just clogging up the system, learning to become criminals. I think we should save the jails for the actual criminals and avoid, if we can, drumming up business.