In the US in 2010, cost per inmate per year in a state prison ranges between $14,603 (Kentucky) and $60,076 (New York), and averages at $31,286. That's 16 years ago, so it'll be higher now. In the UK it was an average of £32,315 in 2020-21. You might as well employ an individual case worker, and the societal outcomes would be a hell of lot better.
As one of my friends remarked to me it's not a healing environment. The staff there, in my limited experience, vary a lot in their attitude. Some of them are great. Some not so much. It depends who you are dealing with.
True, but we have institutions dedicated to dealing with people like that.
A school isn't that kind of institution and will fail in its mission (to protect and educate) if it tries to fill the role of controlling violent people.
It's similar to how prison is a deterrent to crime. But it doesn't change the fact that there are people who still do crimes and get into prison.
They may be bullies themselves because of an ongoing toxic culture in the school. That can include the teachers in some cases, who are some of the worst bullies in there. I had one who persecuted me for a speech impediment and humiliated me in front of an entire class of children by making me say tongue twisters.
None of what you said contradicts the above.
Expulsion isn't going to reform them, it will just move it on elsewhere.