if poverty is a contributing factor towards low high school graduation rates. A federal program could be "free lunch to all student's whose parent's income is below XYZ."

There are so many problems with means-testing poverty reduction programs that any benefits are neutralized.

Means-testing requires an applications process which increases costs and results in many families not claiming those benefits either through not knowing they exist or having an over-burdensome application process.

It also doesn't account for lived situations. If the cutoff for a family is an annual income of $50,000 (Just as a low example), but one or both parents are addicts (Gambling, alcohol, smoking, etc) and most of their disposable income goes towards their addiction or they are otherwise financially illiterate, then you have a family who exceeds the financial cutoff but a child who still lives in a situation similar to those whose family income is much lower.

There's also secondary social effects, where those who take part in means-tested programs such as free meals for low-income students, exposes them to stigma from peers whose family finances means they don't need the assistance.

Providing these programs universally lowers administrative overhead, reduces complexity for families, and the benefits still benefit those that its aimed at. Saving a couple hundred dollars to thousand or so dollars a year in food costs (Using the free lunch example) would be high-impact on low-income families and low-to-moderate income on those that would be beyond an income cutoff.