There's no a priori reason you would expect student expenditures to become less effective per dollar in richer countries, except the fraction spent on labor.
Education is almost entirely labor and real estate. It’s a classic Baumol’s cost disease situation. Like I guess richer countries can purchase better computer labs?
So yeah, it’s probably true that the US spends more per pupil because we have a higher GDP per capita, but it’s not clear that we should expect to get a lot more out of it.