Human Capital and Investment into Children Famous labor economist James Heckman made the argument that given money for investing into educating people, we should invest into young children, and pretty much only that age group, because they have the most periods of time to compound human capital over time, and arguably get the most benefit from it. 

http://jenni.uchicago.edu/papers/Heckman_Masterov_RAE_2007_v29_n3.pdf

Obviously it's a pretty strong argument, and I was wondering what sort of research in the literature you might find important that takes the stance against this sort of idea. My intuition tells me that we'd want to smooth investment into all sorts of age groups of people for some sort of externality reason.
You ask for studies which I don't have, but I can think of a few reasons:


Diminishing returns - if a child has a decent home and parental support you can give them a good education at reasonable cost. To get a child from a broken home to the same point requires much more intervention - and cost.
Moral hazard - there are many hard-working families just above the breadline. The parents go to great lengths to ensure their children have a decent home. It may be that they get no support for all this effort - but if they simply stop making an effort, the child then gets massive support from school.
Need for high achievers - for society to achieve (cure cancer, explore space, win wars, etc.) there is a need for high achievers. If the education system focuses entirely on getting under-achieving children up to average, this comes at the cost of high achievers.


I'm from the UK, where there is an extensive welfare system and extra investment in education in deprived areas, called the Pupil premium. Although, not nearly as much as suggested by the paper you reference. 

Many people do not support the pupil premium. There is a large "squeezed middle" in the UK, not poor enough for extra support, not rich enough for private schools, and this group sees extra support for deprived areas as unfair.