The icon for the Remove Header command always has a red X, because it's just part of the icon:
It doesn't mean the command is disabled.
When a header contains any text or image or anything else, then the Remove Header command removes that content and leaves an empty paragraph mark. (That's exactly what Stefan's macro does, too.) It emphatically does not "remove the header" to leave nothing there. If there is no content in the header (except for the empty paragraph mark), then the Remove Header command doesn't make any change.
If you really want to get rid of the header, click the little button in the Layout > Page Setup group to open the Page Setup dialog. Go to the Layout tab of the dialog and set the Header measurement to zero.
You can restrict that to the current section or let it affect the entire document.
P.S.: In Word, "page breaks" and "section breaks" are entirely different things. To remove sections, you must have deleted section breaks. The headers, footers, and settings of margins, orientation, page size, and columns are stored in the section break at the end of the section. https://wordmvp.com/FAQs/Formatting/WorkWithSections.htm