In the home page of Phoronix.com, the screen reader, NVDA for Windows, does not understand that HTML5's header tag is for the title of every articles listed in the home page. When I visit an article to read everything below the heading, I press H and NVDA told me there are no headings in the web page. I then tried Shift+H to learn if there are any previous headings for this web page and there are no headings at all.
The use of header tags are not treated as table of content for outlining the entire web page. H1 should be your logo of your website that takes you to the home page. H2 should be the title of the articles that follow before an excerpt. If there's a section of the article and you want to give it a title for the particular section, then it would make sense to use H3.
Does that make sense?
In my opinion, you are setting yourself a bad example of how you code your website that takes full advantage of HTML5, yet you did not structure the web site properly in order to accommodate screen readers such as JAWS for Windows and NVDA. There is an Orca screen reader available for Linux, so you might want to give it a try. If you can browse the Internet using your keyboard and without your mouse, try to navigate your website through headings by pressing H and Shift+H. You can also use 1 through 6 below function keys to cycle through different levels of headings.
I hope I can be of help and will look forward to seeing your response.
Thanks,
--Grayson Peddie