Too many armchair educators here. I literally teach a lecture on this as part of a class on students with disabilities. Key things about DoE:
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It's 4% of the budget and 2/3 of that is to subsidize higher education for middle and lower income families. For K-12, it's about 5% of the budget, as most funding is state (unfortunately usually by property tax, which generally fucks poor folk).
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To get that 5%, you need to play by DoE rules. That includes no discrimination, school must be free and accessible, and you need to follow IDEA, the law that gives students with disability access to an education. Without federal DoE, there is no standard requirement to accommodate kids with Autism, learning disabilities, and more. (Technically section 504 can still apply, but it's complicated. Private schools usually have that but not IDEA). Btw, about 100B + 20B for K-12 funds and disability, respectfully.
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DoE funds and conducts a ton of research that improves pedagogy, not just the standard NCLB achievement tracking but things like the ELS database that is one of the few sets with data from 10th grade all the way to age 30, to directly analyze effects of high school programs on long term success. My dissertation used that, and yes, those folks are probably super-illegal fired, USAID style. If you're wondering, it's 800M in grants and research, which is chump change.
Understand, this is as idiotic as gutting the IRS. Economics have found that return on investment is tremendous (8x to 60x depending on who you ask) because you reduce crime and expensive prison costs. Simply preventing a murder saves millions of dollars, and education is shown to do this (including the very same ELS data I mentioned!)
There's more that I can say, but if you have questions, I literally have a degree in education policy. Please ask!
