Except you run into a few problems when implementing that, especially for public schools.
Proactive parents will typically want their children in good schools, regardless of their child's behavioural history. (This doesn't mean they refuse to acknowledge the issue, though some will. It simply means they want their children to have access to better supports.)
There is an overarching philosophy within the school system that integration is better than separation. I don't know if this has to be the case, but it has been historically true. Think of it this way: even though some of the best teachers may want to serve the most challenging schools, good teachers almost always want to teach in good schools. Where does that leave the challenging schools? If they're lucky, with a great teacher. More often, with a bunch of mediocre teachers.
Related to that, schools rarely have the resources to distinguish between students who would benefit from integration and those who would benefit from specialized and separate programs.
I don't think you should segregate schools. Just classrooms. That gives students in 'bad' classes something to aspire to, and keeps them on the map rather than being written-off to a 'poor school', and parents should realise that, though their kid is in the 'bad' class, they are getting appropriate help, not just being discarded.
In some ways, the 'best' teachers should be assigned to the 'bad' kids, certainly those with the best command of a class. The 'good' kids don't need that so much.
These kids are still going to be on the bus, at recess, or at school functions. Not sure if you were ever bullied, but all three of those are prime locations due to lack of adult supervision.
I mean bullying is a thing worldwide to some extent, but I think America needs to fix it's high school culture. If not it's entire, aggressive culture.
I think you still need something to incentivise the best teachers to voluntarily sign up for the lowest performing classes. Obviously its way more prestigious to be the teacher with all the ivy league destined students than the teacher whose students are just trying to get set up for a community college or a blue collar apprenticeship. [This is not to say the latter cohort is less intelligent, capable, or important-- just less prestigious.]
I see teaching these kids as a specialization in itself, so the incentive is to be a great 'turnaround' teacher, plus the pay should reflect that it is a difficult specialization.
The right answer is probably to pay the teachers of the problem kids more or adjust student teacher ratios- For example, with no behavior problems a single math teacher could probably handle instructing and grading 50 students, as this is the model in college calc.
For what it's worth, in New York City the Gifted & Talented classes are often larger for this reason. A 2nd grade G&T classroom where I was a student teacher had 30 students, for example; standard classes at the same school had ~20 students per class.
I think you do want the "good" kids to be taught by the best teachers. That way they'll have better chances to succeed and you won't have so many good teachers get burnt out. I think people should just normalize sort of giving up on the "bad" kids and send them to the delinquents school or military school or whatever. The whole idea of having the best teachers teach the "bad" kids is completely wasteful of limited resources.
"Proactive parents will typically want their children in good schools, regardless of their child's behavioural history"
Why wouldn't this apply to private schools especially because in that situation parent's have financial leverage?
Edit
Another comment said that private schools have an incentive to provide a good service otherwise people will take their money and leave. I want to temper my statment about parent's changing schools because
1. Unlike grocery stores or gas stations how many schools would be within reasonable distance where a parent could easily change.
2. "Customers take their money and leave" doesn't seem to happen that often with every other business. It's a constant theme here where we complain about the general public continuing to use substandard products. Yes it's a serious product (child's education) but factor in my points.
3. Changing schools could be traumatic for a child because they made friends, comfortable with teachers, familiar with the school. School isn't where you buy gas or go to the gym. Children are young AND emotional, stability is probably ideal. This means parents don't have as much leverage as I first stated
4. What metric do parents use? Grades, bullying?
If grades schools will have a financial incentive to inflate more than public schools. Public schools and private both have standardized tests, however a report card from a private school is a subjective judgements from the teacher that the parent will use as a metric
If bullying and a parent complains once should the other child be expelled? How does this system work? What if there are no witnesses,
bully denies it. What about verbal abuse, what if no one hears it?
If private schools start expelling bullies why aren't they required to teach children like public schools. Charter schools are supposed to be about a parents choice why should a child, bully or not, have less rights especially since they receive public money.
Proactive parents will typically want their children in good schools, regardless of their child's behavioural history. (This doesn't mean they refuse to acknowledge the issue, though some will. It simply means they want their children to have access to better supports.)
There is an overarching philosophy within the school system that integration is better than separation. I don't know if this has to be the case, but it has been historically true. Think of it this way: even though some of the best teachers may want to serve the most challenging schools, good teachers almost always want to teach in good schools. Where does that leave the challenging schools? If they're lucky, with a great teacher. More often, with a bunch of mediocre teachers.
Related to that, schools rarely have the resources to distinguish between students who would benefit from integration and those who would benefit from specialized and separate programs.