As far as I can tell, the Department of Education's role (https://www2.ed.gov/about/what-we-do.html) is largely limited to certain funding (eg: student loans), statistics, certain anti-discrimination legal enforcement that is applicable at the national level, and "[identifying] major issues" (eg advocacy). Plus some items related to the No Child Left Behind act.
A lot of that seems okay to me. In particular, I think having a centralized statistical department (what this department's role largely was before elevation to cabinet level) is absolutely worthwhile. Student loans would in my opinion be the most interesting topic to explore of the above, but it's more or less worth a debate over it... not "eliminate department due to Reasons".
The question isn't if the ends are desirable. It's whether it is acceptable to merely consider whether the DoE as currently-constituted is the best way to achieve them.
/s
I had a fairly sheltered upbringing in the UK, but we did at least do some world geography and the GCSE curriculum in the early 90s required a little bit more social geography, concentrating on the southern parts of West Africa (not that I remember much of it now).
Without any world geography at all, well it seems criminal to set up an education system, that way.