The Dept of Education is the primary administrator for school and individual financial aid and funds to state schools.
1. That represents 8% of all state school funding.
2. On an even larger basis, it administers post K-12 student financial aid programs and loans.
If you get rid of it you have to replace it immediately with something else to administer that, unless you want to get rid of Federal aid to state school and post-secondary aid to students. If you want to do that, you'd better bring friends. A whole lot of friends.
Can you make it more efficient? Sure. thats not getting you 1/3 of the US budget.
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Targeting higher education is an essential tool in the autocratic playbook