This is kind of backwards. Because of the way that education is funded in the US, expensive housing areas end up with good schools because they have the funding

This is kind of backwards. Because of the way that education is funded in the US, expensive housing areas end up with good schools because they have the funding. And people live in these expensive areas because they have the means and desire to live in an area with others of their same social status, or and/or whose reputation confers status.