But you are correct! This way of showing off your work is much nicer than what ends up in the paper. The blog representation is a good opportunity to show off the results of the paper on a higher level. However, the "mathy" paper is still important so other experts in the field can understand the details of the technique
Wanted to clarify that this is the summary article of the paper. I wrote it to help out people who might not have the math rigor and research background to understand research papers but would benefit from an intuitive explanation.
I would argue that folks like you translating the heavy science into comprehensible ideas to those less deep into the field are doing just as much to advance science as the authors of these papers.
Seriously, this is fantastic work and I cannot compliment you enough on it.
Speaking of diagrams, I once read a short (probably no more than 3-4 pages) paper with one theorem and one diagram. The diagram was essential for me to understand the proof. The problem was the diagram was a diagram of the proof.
That is, plenty of good diagrams, clear explanations and intuitions, no unnecessary mathiness.