They need to raise some of their own funds. They have to recognize parental expectations. Increasingly, they have to be responsible for results. The public schools have to train the workforce, integrate the population, counter hunger, violence, disease and other effects of poverty, provide child care, and render moral counseling. Earnest efforts by the cheerful staff won't make it work.
Independent schools run the gamut.
Some are merely exclusionary versions of public formats with boilerplate content and standardized processes. Traditional and ideal notions of a liberal education which includes art, drama, literature, philosophy and language are subordinated as extras. They have essentially good people running them in a generally good way with some ideals but few intentional outcomes. Religious schools know what they are doing. Hence the extraordinary and intimidating power of such groups.