Oh, I never meant to imply that it wasn't worth applying; you never know what you'll be offered. What I meant to point out was that one should not count on public/private costs working out about even or better.
It seems to be a common idea here that private schools have so much more money that they almost always even out with public costs, and that is much too simplistic an idea. I depends entirely on your state. In the Deep South, in particular, you are unlikely to be able to beat the cost of one of your state universities (perhaps not the flagship, however) with private-school student aid unless you get a full ride, or if you can live at home for the private vs. living away for the public.
Now, if your family income is low enough to be eligible to go to Berea or College of the Ozarks, or another school of that sort, then they should definitely be encouraged to consider them. Those are both excellent private schools that cover full cost of attendance for all students via work-study programs.