Some public charter schools do the exact opposite, take in the problem kids so they can be given an environment better suited to their challenges. For example, Gateway Highschool in San Francisco. And they have better outcomes for those kids. But better is relative, and they get alot of criticism from those convinced equity demands the whole student population be perfectly shuffled across all classrooms, and who argue having such options excuses the district from providing even more resources to the average classroom. Many of those same people also work to prohibit ever removing a problem child from a classroom (see recent controversy in SF, about schools secretly doing that despite city prohibitions on suspension or even class removal), arguing instead every classroom should have 2 or 3 additional instructors, as if that would magically cease the disruptions.