There's the entire reason: the Catholic schools' success is an embarrassment to the supporters of government education monopolies.
More than twenty years ago, I read an article in New York magazine in which it was said that the paperclip budget of the NYPS exceeeded the total administratice cost of the archdiocese central office. The public schools suffer greatly from overmanagement. Even paying teachers $100,000 does not mean that the money goes to teach English and math. the classroom. After all, each class of 30 sixth graders brings $450,000 into the school system.