That's a rather open-ended question...
Schools participate because it is morally right to give their students a chance to learn about science and technology. There is no curriculm out there that as closely emulates the engineering industry the way that FIRST does. It's not even so much having students read a book and take notes on sub-assemblies, but teaching them how to work out problems with people from differing backgrounds.
FIRSTs focus is (I believe), not so much developing engineers, but developing leaders. However, their hope is that after they've developed a leader, that leader will use their skills towards strengthening the American scientific and technological community.
The purpose of High School is to help a student develope the skills necessary to be successful in life. Schools strive to do the best job they can, because they know that in-turn... the better student they produce now, the better citizen that student will become later. The english class, math class, gym, history, and sports teams do a decent job on their own. But throw in a program like FIRST, and those students who participate in it will have a world of opportunity at their fingertips.
Take me for example, I'm living proof
(my life is like one of those formula live-action disney original movies)
ByE
erin