If you want relatively equal access to education and ensure minimal gap between poorer areas and wealthier areas, then there is no alternative other than a centralized education system where tax is collected federally and funding and initiatives are driven by comprehensively studying the needs of the whole country.

Just like many other things in this country, the distributed, State/local based education system simply does not scale for the 21st century.

The reason we are wasting so much money in education is despite the total cost, due to the siloed/localized system we have, we can't effectively direct funding to places that need it most. The federal government can spend tens of millions doing some "study" in why education sucks in rural schools, but it can't use a penny of that money to actually pay salaries of teachers in rural schools. In some other countries you have national programs where they pay young teachers extra to go to less desirable areas to teach, and that's just one minor examples we can learn from.

And that's not counting the whole federal budget. Just imagine how many school districts like the one from this article we can save if we just build one less Ford class aircraft carrier.