I think this is a really good point. While I like the article's focus on depth, and thinking about the small stuff is important, saving a few bytes on headers is going to be blown out of the water by all the images, JS, CSS, and 3rd-party pixels being loaded. "Profile before optimizing" applies here too.
But I bet you most people will never profile this.
We have a tendency to focus on page size but what really matters is the user experience.
For all the advice of putting making sure the first 15KB of a page counts, inlining critical styles etc., it that response has 4KB of headers e.g. large cookies, then all of a sudden you've got 11KB!