I think that essay completely misinterprets the imagery of the guillotine.

Why the guillotine is a popular image is:

1. It’s strongly associated with a time of revolution when the ultra-rich oppressors were executed. This has happened many times throughout history and in many ways, but a gun, a firing squad, a noose, a spear, etc. all have other connotations. The guillotine is remembered primarily for the French Revolution and for how it was used to execute the oppressors.
2. It represents judgment, not chaos. That isn’t to say that there wasn’t a lot of chaos in the French Revolution, and it doesn’t mean the judgment was fair. But, it’s the kind of execution apparatus that you basically need an organized group to run. It’s big and clunky. So, if you’re in a position to use a guillotine on people, it means that you’ve already taken power, and probably have some kind of process of a trial before executing someone, even if it is just a show trial.
3. It’s very final. Look what happened when the French didn’t use the guillotine on Louis XVIII or Napoleon. Louis XVIII went into exile during the French Revolution. After the revolution, Napoleon reigned as emperor for a decade, was exiled (not guillotined) then Louis XVIII took over for almost a year, then Napoleon escaped exile and took over again for 100 days, then Louis XVIII was back in charge for 10 years. Say what you will about the guillotine, but one guy who never took power again was Louis XVI.

Do people think that a literal guillotine will solve all the problems? I doubt it. But, it makes for a powerful symbol. It’s saying “deal with the ultra rich / ruling class, in a state-sanctioned way, and permanently”. It’s not a symbol of compromising, but it’s also not a symbol of mob violence like a noose hanging from a tree would be.