Because if we’re just guessing, I would guess elimination of private schools would result in rich people with children grouping up in very wealthy areas more than they do today. A public school in a very affluent and wealthy area would likely not have many “pools” attending (because the cost of living in the area is so high).
One other type of charter school to consider would be one’s specialized is students with various disadvantages such as charter schools specialized in blind, deaf, autistic or emotionally disturbed students.
This 2018 analysis by the NCSECS (national center for special education) found that there were 137 such specialized schools and many were primarily focused on students with 1 specific disability. These schools had high enrolling rates for such students and found they had lower rates of suspension and expulsion. The recommendation was additional funding for such schools.