This only works for exclusive, high prestige schools. Not many rich foreigners are going to pay full freight to send their kids to Western Kentucky University.
America itself and the opportunity to get your foot in the door with a student visa is the prestige factor for many students - the prestige of the university is secondary. That allows a lit of third tier universities to fill their master's programs with international students
The community college I used to work at made its bread and butter from foreign students. Super mega rich parents sent their kids there. Many of them drove expensive cars. Community colleges in the US are actually highly regarded in a lot of places overseas, believe it or not. And this wasn't in some big city either. It was in kind of a town that isn't very well known for being a safe place to walk around at night.