I know the reason why, because it makes the page cluttered, whereas having it at the footer does a better job of hiding it. But isn't that the exact problem that the hamburger menu was made to fix?
And by "accessibility" I'm quite certain the author means "usability for people with impairments that don't allow them to use a mouse and keyboard or touch screen".
The article discusses the problems of a hamburger menu but doesn't address why its used, and then goes on to suggest a solution which does a worse job of what the hamburger menu is actually designed for.
You asked "Why put a link to the footer in the header which contains links to other pages when you can just put your links directly in the header?" The article answers this question, quite clearly and in detail.