If you want to see how an egalitarian education system reaches the best education system results in the world - Estonia and Finland are the countries to look at. Their education indeed follows the second model here. But rote learning is also included - the point is to challenge and support the child in manifold ways and keep in mind that they should enjoy themselves.
My point is though while in some countries this might be a class difference, really it comes down to a quality difference. Good quality does not actually need to be very expensive/rare, you can reach it at system level as do Estonia and Finland.