So the federal government does have some real control over the education system. One of the things it's done with that control is impose mandatory standardized testing, with funding penalties for poor performance. The stated goal of these tests is to ensure that all students are acquiring at least a certain basic skillset, which seems noble enough, but the monetary rewards and penalties create perverse incentives for teachers and administrators to teach to the test, prioritizing test-taking skills and narrow rote response over a broader skill set and deeper understanding of the material. It also creates a feedback loop whereby the rich get richer, as it were, while under-performing inner city schools who arguably need the most help get punished with cuts.
So yeah, we could argue about exactly how much of the problem is federal and how much is local, but the federal government absolutely has exercised power over the education system and deserves its share of the blame. The one thing I'll agree on is there's not a ton the government can do about it, but that doesn't stop it from meddling and I'm pessimistic about the results.