How is capitalism the thing valuing teacher's salaries? If referring to the US and public education, aren't they a branch of the government? And even ignoring

How is capitalism the thing valuing teacher's salaries? If referring to the US and public education, aren't they a branch of the government? And even ignoring that(for example, at private schools), the 'consumer' here is really the parent. The child isn't in a position to choose schools, so it's really about selling to the parent. I imagine it has to be hard to get a sense of any 20-year projected ROI if you can only indirectly measure teaching quality by what your child says and standardized test scores.