I think having the header accessible at any point of the page without having to scroll all the way up is important, since pagination is a concept of the past and you might be at the bottom of a long topic, but the header does make the viewing window significantly smaller. (It takes up about 10% of my 13" MacBook Pro screen.)
I noticed on Medium that they started hiding their header while you scroll down (and are presumably reading), but it appears again when you start scrolling up. Here’s a link to an article, just so you can see.
Perhaps this would be a good approach to adapt for Discourse?