[gostsamo]

Honestly, I have limited time and writing extended counterpoints to every argument is rather tiresome.

Regarding the article given, what made impression to me was that it states that if a document have a few important articles, all of them deserve to be h1. Well, put h1 as the topic that binds together those articles like "The blog of an expert" and each article can move to h2. Simple, semantic, and does not need to break convention.

I'm not against a few h1s in a document, but each of them must be important in a different way like name of the website, name of article, important warning in the footer/sidebar/wherever. It is like mail, if each email is marked "important", none of them is or at least you can't make your mind without reading everything and deciding for yourself which makes the "important" label meaningless.

Edit: adding a counterexample.

I've visited news websites which have sidebar with most recent or most read or the like articles. Each item in the list is marked h1 and skipping them wastes time and money.

Same with a few sidebars that are h1 titled though I don't care about their existence and their presence just shadows the h1 of the article that I'm interested in.