I hope the Department of Education does get eliminated. With more state and local control, there will be more freedom to shake things up and make changes that are custom-molded to each state and each district's needs.
Also, if enough people in a town prefer to homeschool their children or send them to private schools, that town should allow their residents to vote on abolishing the public school district completely. Then the town can spend more time and money on other things and/or cut tax rates.
Here's something else that bothers me about the way public school districts are run. If you're the mayor of a town, you have the authority to fire the chief of police or the fire chief or the head of any other city department if they're doing a crummy job, but you can't fire the school district's superintendent. That's the job of the school board, and the school board members are elected by voters instead of selected by you. Sure, you can vote school board members in or out of office, but your vote is meaningless unless enough people vote the same way you do. The only power you as mayor have over the school district is to adjust the budget. Maybe public schools would be better if the mayors of cities were able to fire the superintendents of their school districts. Just a thought.