I've literally been doing nothing but studying chemistry and biology all day, so I can't give a full cogent response right now because my brain is almost completely fried, but asian countries have lots more wealth disparity than the US. This isn't even debateable. If you're cherry picking Taiwan, Japan and South Korea while ignoring Indonesia, Singapore, Thailand, China, India, Cambodia, Laos, etc. by declaring them "undeveloped" so you can pretend they don't exist, then you're introducing a large amount of bias into your evidence, because China and several others on that list most definitely qualify as developed nations.
We could do better, but we spend 80 billion a year to the Department of Education. With our budgets it could always be more, but its hardly starving the beast, as it were. The idea that government would ever willingly
1. Privatize education when its the best way to brainwash your population into believing all sorts of nonsense
2. Privatize education and thus limit the bureaucracy that insulates and sustains bureaucratic power in the organs of governing powers
Is almost as crazy sounding to me as the idea that reptiles from Glaxxon 5 secretly run the planet.
The idea of privatization of education isn't my favorite, but it does produce good students, and I do think forcing parents to have some actual skin in the game they can feel, some cost to them directly to educate their child, might spur them to take a more proactive role in their children's educations. The driving force for parental involvement in children's schooling in Asia comes from the fact that the parents expect the child to help provide for them in old age when they can no longer work. By having skin in the game, their futures literally on the lines of their child's success, it does compel the parents to care a lot more.
Not saying we should go full asian system, but pointing out that there are certainly things we can emulate in our own fashion that would probably help.