And speaking of Cato and economic complexity:

As his income grew, Cato also became a regular investor in commercial lending. Although a law from 218 BC banned senators from engaging directly in commercial shipping, Cato formed partnerships of fifty investors that backed the commercial operations of fifty ships. He fronted all of the initial capital and then lent money to investors that they could each use to buy a share in the enterprise. Cato himself entrusted one share to a freed slave who acted as his agent. He then profited from the trading activities as well as the interest on these loans, while following the letter of the law and limiting his direct exposure in case the cargo was lost.

I'll just leave this here: I think the destruction of Carthage was a great catastrophe. Both for the world from a humanitarian perspective and for Rome which squandered a lot of economic generativity.

And now, Moskva delenda est.

That was my first thought. Playing Civ games and reading books like Prisoners of Geography makes it pretty explicit

I’d argue that a complex economy in a failing society is actually a sign of weakness. Lots of nobles and the likes wanting their cut of a pie that doesn’t really exist anymore. So all of that complexity is not really backed up by the reality and you just have a bubble. I can imagine all kinds of roles and professions that just exist to endow people. This also happens a lot in modern society.

I know this wasn’t actually your point but I just wanted to add.

Which is why the title explicitly names the Western Roman Empire, and the article briefly discusses data issues with Greek inscriptions near the end.

No, based on the professions named within the inscriptions. If a province has relatively many professions that are rare for the WRE, then it's considered more complex. See the paper for the actual estimates, the map in the article does not show the complexity estimation

Same here - I suppose this article did what it was supposed to do - give a short primer introducing the topic and if you want to see how they computed this look at the paper!