What does inequality even mean? Everyone must be identical? The idea of removing inequality is dystopian.
You could do this right now with a lot less money then it seems, the problem is that you have to break ethical grounds - for example, you have to have police or support staff that forcibly take kids from their homes if the parents resist this sort of education for their kids. If you don't do this, then you essentially are back to square one.
Aristocrats are going to aristocrat, as they say.
Early United States was pretty good but having a western frontier with "free" land was probably the enabling factor that no longer exists.