@joefromchicago,
yes and no - they did provide benefits to underprivileged students, free or reduced tuition - they did not have buses (it doesn't make sense for smaller schools), but they have other things that public schools did not. The teachers had many benefits including 100% free tuition for their children.
My public school does not have security other than the same my former private school had - basically the office and a locked door with buzz in. The class sizes in the private were significantly smaller so they offered more individual attention - for example my daughter was ahead of the other students in one class so she got a specialized academic plan.
The private school offered many academic opportunities than the public: math olympics, spelling bees, geography bees, etc. And musicals each quarter. All paid for by the school and included in with the tuition. They had a dedicated art, computer, music, gym, language teacher - even with only having a little over 100 kids in the school.
If anything you would think the public schools would be able to take advantage of their scale. You would think that one art teacher for 400 students would be cheaper per child than 1 art teacher for 100 students.