I'm not a civil engineer, so I have no intuition for these types of things. But I'm certain I wouldn't have guessed that the limit here was 3km! My mind can't even visually picture a thing.
Note that after this quote, the article immediately discusses other constraints, including lateral loading, which dramatically reduce the upper limits. But I'm still boggling over the idea of a 3km tall tower -- it seems like it would just sink right into the earth!