First is that the federal government doesn't have the legal standing to take over the education system. I believe it would require a constitutional amendment to allow it and I don't think they'd get that passed.
Secondly, I'm not sure it is such a great idea. Currently federal level education direction comes from the teachers union and you can see the fruits of its labors in our current schools. Also I think this will make the current broken system harder to fix as it will institutionalize many of the current practices and make local experimentation much harder.
IMO what we need to do is move away from the industrial revolution era school system. We aren't training a bunch of factory workers anymore and that needs to be reflected in how we teach. We really need to do a lot more trials with alternative educational styles in public school. My understanding is that one of the biggest hurdles to this is the teachers union and their adherence to the current model.
I do think funding is an issue, but even if you could magically fix that you'd still have bad schools. There would just be less disparity between them.