Even when there is some subsidising towards educating children that are unfortunate enough to have poor parents, you still end up with very unequal outcomes.

Go down to Figure 53 of this: http://www.nzchildren.co.nz which shows only 1/3 of the poorest 20% attain a high enough level of education to even enter university, while 3/4 of the richest 20% do (the relation is fairly linear for the rest).

Financing the education of children with poor parents helps, it just doesn't equalise on average. Of course it does help a few outlier children a lot.

In NZ we add extra subsidies to schools with poor parents through a system of deciles - but it doesn't offset the difference that much.