Schools are not underfunded. The U.S spends more per capita on education than pretty much everyone: http://rossieronline.usc.edu/u-s-education-versus-the-world-..., twice as much as South Korea.
Dances/events are usually funded by fundraisers. Although an exorbitant amount of money is spent on sports, they also have a lot of funding from booster clubs and fundraisers.
Schools do get stuck paying for extra sports staff, and sports facilities. Sometimes a wealthy donor will spring for a giant football field. That actually sets a bad precedent, because then neighboring towns feel they need to spend more on their sports facilities.
Arts and music programs receive almost no money from any source and are cut every year.
It is assumed that your success in life comes from your relative standing, your percentile in the forced ranking, not from your absolute level of education. Both the public and the private education systems optimize for getting their students as high on the relative ranking as possible, not for training each to be as valuable as possible in terms of what actual services he can provide to his family, his employer, and his society.
It is often assumed (around the world) that the former will yield the latter. In other words, competition for ranking will make everyone more valuable. This is only partially true, though. The ranking is a one dimensional aggregate of a few dimensions that are easiest to measure: solving math problems, answering trivia questions about English vocabulary and grammar, remembering historical facts, and so on. This causes those few areas to be over-invested in, hence others to be under-invested in, relative to their real ability to produce value for self and others in adult life.
The real economy (not just money but quality of life) is far more diverse and multidimensional. Post-primary-school education would be better if it didn't force everyone to focus almost all their time and effort on maximizing the same three or four dimensions.