Full federal control would be the Feds deciding what text book is used, letting them decide what and how to teach hot button topics. Letting the feds decide what is taught in sex ed, what is said about evolution, about religion about government. As it stands localities have a great deal of control over what gets covered and how. I've never read anything that suggest federal involvement in well funded districts has any net benefit. The less involved the feds are in schools in our community the better in my book.
Full federal control would prevent the Texas School Board from buying 5 million textbooks that teach creationism. That would give every other school board the option to buy books that don't teach creationism. I don't want your book. I want a book that is at least approved by a chain of command I can vote against. There's nothing I can do about Texas books or Oregon books but publishers aren't going to come out with a special edition for New Mexico. I grew up with Texan biology books. They're bullshit. And they're why museums of creationism exist.As a market, the state was so big and influential that national publishers tended to gear their books toward whatever it wanted. Back in 1994, the board requested four hundred revisions in five health textbooks it was considering. The publisher Holt, Rinehart and Winston was the target for the most changes, including the deletion of toll-free numbers for gay and lesbian groups and teenage suicide prevention groups. Holt announced that it would pull its book out of the Texas market rather than comply. (A decade later Holt was back with a new book that eliminated the gay people.)
Or a full federally controlled school system would mandate that you had to have text books that taught creationism. Despite the Texas lock in I never had a biology text book that mentioned creationism. The local school board or state school board decided that you would use those text books because they were the cheapest. We elect our school board here, I don't know how it worked where you were. The more control localities have in the educational system the more likely, not less, that the values of the community will be represented in the classroom. I'm fine with people in Alabama learning creationism as long as it means people in Oregon will never have to.
"My state works, fuck everyone else." Trump won Alabama by 28%. The community will is definitely being represented in the classroom. That's probably why it hasn't really changed since George Wallace was governor - when a pedophile can only lose by 20,000 votes there's some issues with the community. No matter how bad you think it is, most of the country leans towards the middle. It's the fringe you need to worry about. Making the fringe subject to the majority is rarely a bad thing.