Well, if you get to teach a lot of well-off kids who have a lot of extra support at home and you can siphon off the undesirables onto others, you get good marks when most of them inevitably "succeed".
If you have to teach the kids who need help, you get poor marks when some of them inevitably fail.
School choice via vouchers, etc would allow parents to decide for themselves how outcome is measured
Edit: why the downvotes? If you are uncertain of or unamenable to the way outcomes are measured, vouchers are a reasonable solution that puts the power in your hands
2/3 of private schools are religious. And many private schools were literally founded as a response to brown vs board. Parents are not choosing schools based on academic success alone.
An extremely significant part of how parents choose schools is based on the social groups they want their kids associating with.
99% of the academic success of private schools is attributable to their ability to exclude poorly performing students, not some magical pedagogical secret.
It’s the same exact reason why homes of equivalent quality in two different districts of the same school system may have 2x or 3x price differentials. Because parents pay hundreds of thousands so their kid doesn’t sit next to a kid with parents who can’t afford the same.
No they pay hundreds of thousands of dollars so they don't have to deal with the school refusing to take action on bullying or disruptive behavior.
If schools are unwilling or unable to provide a stable learning environment then parents move on. There has been a lot of ink spilled on exactly why this is, including the racial and religious issues you allude to, but the brute fact is that in many communities families flee or switch to religious school because their children suffer violence at the hands of their fellow students.
It's the same thing, phrased two different ways. There's not some magical action any school administrator can take to make poorly raised kids behave. Especially in an understaffed school. You can make them leave the school, which removes the problem temporarily, but then what? Truancy is already a problem, expelling more kids is not going to fix the problem. The US already has one of the largest criminal underclasses on the planet. Fixing a classroom by ignoring tough situations just kicks the can down the road. Your kid will have a nice classroom experience, and when they graduate, they'll be robbed by the kid they didn't have to sit by.
IMO this entire problem was caused by segregating our schools to begin with. The problem of misbehaving kids isn't going to be fixed by giving them free vacation on the streets. They need to see with their own eyes that their behavior isn't acceptable, and that means putting them in environments where they are outsiders. Kids are a product of their social environment, full stop.