I have to disagree with your contention that an obligation of the state is entirely due ot the right of the recipient. That may be where we're at loggerheads. There is a distinct difference between the state obligating itself to a goal (say... national defense) and the right of an individual to compel the state to take that action on their behalf (build an interstate highway to my door).
In this case, the state(s) have commited to provide an education system "being necessary to good government and the happiness of mankind". That means they've signed on board to provide a school system. Doesn't mean they have to let you in, or keep you in if you don't get good grades, or misbehave. The legislature can set up the rules however they want to, unless there's an overriding document (like a constitution) compelling them to do things a certain way (and a judiciary to hold them to it). In many instances, state constitutions require "free and open public schools", meaning anyone can go and they don't have to pay.
However. The state legislature could write a bill tomorrow saying that their obligation to fulfill education will be discharged if they provide a 3rd grade enducation free to all, and then choose to have a competitive process for all higher education. Under the theory that higher education should be reserved for those likely to attend and graduate college, and that others should enter a trade, and trades are the responsibility of trade unions or private trade schoools. Oh, and the Federal gov't can keep all their funding, the 'streamlined' system wouldn't require any federal funding.
At least in Virginia, that's perfectly plausible, and nothing that could be done about it until the next election cycle. Not complying with No Child Left Behind? well leaving the federal money on the table removes that requirement, because federal involvement in education is tenuous at best. Federal courts under Equal Protection Clause - not an issue, the system is administered fairly. State courts? well, the legislation isn't unconstitutional, because the VA Constitution allows the legislature to set eligibility and age criteria (without restriction - I'd be willing to bet the original system was for children of landholders only...).
If the US Congress took it into their head tomorrow to repeal the Individuals with Disabilities Education Act (IDEA) - which they're perfectly within their authority to do - then overnight 90% of the 'rights' of special ed kids around the country would evaporate. Considering current state budgets, I have a feeling by default those kids would be warehoused with just enough attention to ensure they didn't suffer bodily harm. Their 'right' to a (free, appropriate, effective) education could be stripped with a single legislative act at the federal level. States were abominable at special ed before federal legislation (of questionable constitutionality...) was enacted to compel the states to provide a real education (never mind a healthy environment) for kids with disabilities.
If you think this sounds ludicrous, consider what Europeans think of our CURRENT education system. My nephew is an Irish citizen, and he gets a free (almost entirely) education through college. Not fully a right, but current law in Ireland. I was in Germany during high school, and college students in Germany _have a right_ to compel their parents to materially support them (as in, food, rent, and transportation - whatever a court finds 'equitable') while they're completing their college education. Those are rights.
Although, reading the Irish Constitution (graciously provided ALSO in English), again the Irish set up a bunch of rules surrounding provision of education and an educational system, but don't actually vest children with an affirmative right to education. Again - very odd. Seems the world has difficulty actually recognizing the children are human beings and deserve rights, and might find means to enforce those rights.
In short, a brief evening's sojourn through US legal code, case law, and various constitutions (state, US, Irish) leads me back around to the same (though more refined) conclusion. The State (capital T capital S) has obligated itself to an odd patchwork of responsibilities to provide education to the population "as a public good". At the same time, The State continually falls short of actually recognizing that any particular individual has an intrinsic/fundamental right to an education (of any description) which they might compel The State to provide for them.
The single document I have seen that explicitly recognizes any such fundamental right is the UNCRC, which the US has explicitly refused to ratify (though in fairness, I believe that's got a lot more to do with reproductive rights than anything else).