Department of education was created in 1867, but was gone in 1868. One year short life. It basically did nothing. You claim there has been department of education since 1867. That is false.

There was an office of education after department of education was gone. But this small office is only about information collection and statistics, which has no power, resources, functions and responsibilities comparing to modern day department of education. Because education in U.S. in 1800s was entirely decentralized, completely on local, church and families. There was little for a small office at federal level can do. You misread the landscape of education in 1867’s America. This is decentralized system just like American college football then.