If society wants public school, that is a school that is administered and funded by the government, then by definition you are choosing to have teachers' salaries decided by politicians and bureaucrats. In order to change salaries, legislation is required. In order to enact legislation, you have to form special interest groups (in this case unions) to represent large swaths of voters, as politicians only listen to votes.
Instead, consider the idea of eliminating public school. With all of the money back in the public's pockets instead of in government coffers, the public could choose to fund education in a manner that each individual sees fit. However, the common argument (and legitimate concern) is that poor people would be left out. Poor parents who don't have the money to send their kids to school, let alone GOOD school, are left raising uneducated kids who then end up poor. The idea that charity would solve this problem is not entirely unreasonable, but it seems to be a cop out.
This is where I think the Khan Academy has the potential to have a major impact. With individual teachers teaching small classes, you're required to have many hundreds of thousands of teachers across the country, leading to an extremely high production cost for education. If instead you have groups like the Khan Academy producing educational materials that are easy to consume, available across a huge breadth and depth of topics and easy to distribute, the production costs for education go way down.
The reason that poor people can't afford private school is because private schools are expensive. Using technology allows organizations like the Khan Academy to produce high quality education at a fraction of the cost. I'd love to see private schools set up to take advantage of this material and educate the public without government involvement and its requisite politician silliness.