Although privatizing public schools would solve a lot of financial issues, it would also give corporations the opportunity to promote their agendas to school aged children. This may have an unhealthy effect on society at large because everything from textbooks to which subjects receive priority would be determined by individuals whose primary goal is to make a profit rather than objectively educate students.
I believe that the USA needs public schools for many reasons, one of the most basic of which is that without them, it would be difficult for this country to hold on to what remnants of representational democracy it still has. Public schools are the key to education of the masses remaining a reality. Without public schools, even the most rudimentary education could very soon become accessible only to those who could pay for it or win it through passing entry tests to take charity seats in classrooms populated by the children of the rich and powerful. Losing public schools to complete privatization of the education system would change the United States irrevocably for the worse.