Let's the take one from #5 in the article. If someone instead of painting this diagram wrote: "Drupal Load Balancer inside Drupal VPC load-balances traffic between Drupal Instances inside two Availability Zones: AZ1 and AZ2" it's way faster to read, more precise, and leaves me without a doubt that I misunderstood or missed some detail.
It's even worse on more complex and busy diagrams. Takes me a while to just visually parse everything, figure out relations between elements, arrows, and even after I scan everything I'm not sure if I understood everything.
On top of it, just creating and later maintaining them is such a hassle, comparing to just editing text.