It is a different mental model
I run a blog and a magazine and I have worked with about 75 writers over the past 5 years. What I've found is that the vast majority of writers—professional or not—do not mentally articulate their stories this way. The long blocks (to use your own words) tend to be the norm and as the editor-in-chief, it is not easy to enforce a more web friendly layout.
The one author who excels in this kind of writing is a certified coach and she is used to prepare information into digestible chunks. Which leads to my second point...
It doesn't always work and shouldn't be forced
Sometimes it simply doesn't. Some pieces are written in a straight narrative arc, in a very informative way, and it simply doesn't call for h2s or h3s. There is no need for steps, or hierarchy. A lot of top trending stories on Medium, right now, are all written like this.
Some other forms (steps to achieve something, mistakes to avoid, reasons why, etc.) really call for this kind of hierarchy and it makes them easier to consume. These are, in a way, more didactic pieces. It works really well for commercial/marketing copy too.
Hierarchy for hierarchy's sake can be counterproductive.
It is a matter of length, too
Finally, I think it is also a matter of length and connections one's brain can make across paragraphs.
The Case for Reparations by Ta-Nehisi Coates, for instance, wouldn't work in a single block. One couldn't just process this much information in one block. Note how pullquotes are also here to break the flow and create pauses in the story.