That may be true, but some would rather not lose the money by losing a student. Take the Catholic school where my mom works and where I graduated from over 25 years ago. The current principal, who was one of my teachers, wants to take in every kind of student and keep on even those who are constant behavior problems, just to keep the money flowing in. My mom predicts that if things keep getting worse, the good families will just take their kids out, making for a loss anyway. She is getting close to retirement and hopes she can hold for a couple more years to get to her 30 years.
I agree; in my area Catholic schools no longer have the luxury of being selective. They are closing so quickly due to low enrollment (due in turn to high property taxes - 75% of which is “public school tuition”), they’ll bend over backwards to keep students enrolled.