I'd imagine there's a more direct financial incentive; if a student's parent(s) decide(s) to pull that student out of school because of a disagreement with the school's administration, then that directly leads to less money for the school.
Meanwhile, a public school doesn't have that direct penalty; if anything, it's just one less student in already-crowded classrooms, so pushing a student out might very well be a net positive.
You are correct. Public schools lose funding when enrollment drops but the magnitude of the funds lost and the degree to which those funds affect the total budget of the school is usually much greater at a private school.
> the magnitude of the funds lost and the degree to which those funds affect the total budget of the school is usually much greater at a private school
Meanwhile, a public school doesn't have that direct penalty; if anything, it's just one less student in already-crowded classrooms, so pushing a student out might very well be a net positive.