I am wary of granting any additional power to a government on any level, state or federal.
Although your assertion that state lines do not change the nature of core fields like mathematics is correct, they do present a change wherein the funds to pay for education sold as a public good are sourced. And my contention is that the federal government is not granted the power to provide funds for public education.
States are left that power, so to the extent that states want to provide/force education to be a public good, they can do so. It is preferable as people could relocate to another state which does not raise tax revenue to publicize education if they so chose to. States, after all, are not prohibited from direct taxiation.
The entire point of the revolution was to shed rule-by-decree systems by imposing the separation of powers through a system of checks and balances. I do not believe that Madison would be of the favor of a federal subsidiary on public education, even in the modern era.
Of course the Constitutional system creates unequal outcomes. Of course it creates unequal opportunities. But those are problems for citizens to solve amongst themselves locally, up to the state level. The federal government is not to squabble in such affairs.
It's not like education didn't exist in the 1700s. The founders were well aware of it and explicitly left it out. The same is true of a federalized Healthcare system.
I genuinely believe that, given no public funding of education at any level whatsoever, we would still see localities mobilize to provide it, as the benefit would likely outweigh the cost. An educated society is preferred, after all. I also believe the solution would be more efficient in resource usage and allocation.