Other public infrastructure issues could be lack of cheap, affordable internet access, clean water, and health care.
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.
I think the idea with funding education more equitably is to remove existing barriers that are created by policy, not about creating totally equal outcomes.
We need a way for improving things where, when a community improves its own space, the gains don't immediately get privatized.