That's not all we're doing. We're also protecting an entire classroom of children from disruptive behavior.
If it's gotten to the point where we would consider expulsion, then some of those children, or their families, likely find that disruption so intolerable that they themselves would need to arrange transportation to far flung school districts. That's why so many underprivileged families are desperate to get their kids into charter schools.
As I keep trying to point out in this comment tree, people seem to have learned that it's morally appropriate to talk about only one type of victim here. I don't agree. I think it's morally necessary to always discuss both the disruptive child and the classroom they are disrupting, always in the same breath.
If you want to argue it's a better distribution, or that there is some reason to believe expulsions will push "problem children" to smaller classrooms on average, then fine, but absent those arguments it's very clearly worse for the student and their parents but not better for anyone else (or rather, it's maybe better for specific other people, but also worse for yet other ones, and on average no better for anyone).
Changing behavior requires pressure and people generally do not like it when they notice it.
I don't know what the answer is, but "all children are owed a public education and in fact we'll arrest their parents if they drop out" and "public schools can kick children out" are self-evidently not compatible policies.