With respect, the onus is on the poster who discredited outcome performance of private and charter schools relative to public schools on account of the "apples and oranges" basis of that comparison to substantiate the claim that private schools exclude "students who are recent immigrants."

Anyone who has attended a private school function involving parents can confirm that the poster's assumption about a lack of recent immigrant students is plainly false.

Something else that might enhance "our understanding" would be to examine some hypothesis  explaining why privileged folk would pay for something that some suggest provides no value.  Either privileged folk make bad decisions with money, or the suggestion that there is no value in private education is misguided.