I wish someone would build a visualizer/teaching tool for structural regular expressions. They are much more powerful than regular regular expressions.

The paper <https://doc.cat-v.org/bell_labs/structural_regexps/se.pdf> is pretty hand-wavey; do you have a tl;dr of what makes them awesome and a tool (aside from the archived g-code repo) that you use to run them?

No hand waving. Structural regular expressions are starting to get popular just in the last couple of years. They're getting integrated in text editors and other tools. Take a look at this talk for concrete examples from the Vis text editor: https://www.youtube.com/watch?v=y41MyOrPt8Q. Also Kakoune text editor defaults to structural regular expressions in the search https://github.com/mawww/kakoune.