Market rates for whom? Programmers? It was never my impression that private-school teachers were paid as well as public school benefits or had comparable benefits.
The reason you pay for private schools is the same reason that you buy a house in a good school district: to select your child's classmates and their parents.
The reason private school teachers get paid equal or less often has more to do with the level of education of the private school. The barrier to every for public school teaching in my state is very high. They get paid a pittance considering how much education they need to have to get the job and unpaid hours worked
The reason you pay for private schools is the same reason that you buy a house in a good school district: to select your child's classmates and their parents.