The DoE has only existed since 1980. American public schooling did just fine without it for centuries. Why is it beyond the pale to consider eliminating it?

It's not beyond the pale, but typically when I hear something like "we must eliminate the Department of Education", it is attached more to a philosophical reasoning (eg: "government has no business in education" / Constitutional arguments / individual freedom arguments) versus arguments over what the DoE actually does.

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".

At least from the perspective of someone who deals with teaching disabled students. The federal DOE determines allocation of resources and ADA compliance of schools. Without federally mandated special needs services many districts could stop offering these services all together.

These just sound like laws that should be enforced by the courts and the regular legal system. Why do we need an additional federal bureaucracy to administer them?

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.

Who else would enforce standards in geographic education?

/s

Presumably it was the responsibility of the individual states?