I was confused when "knowing a broad array of mathematics" wasn't the focus. The article ended and I paused to ask myself "what did this have to do with polymaths?" - Trying to follow my intuition from "polyglot" to "polymath" failed me here.
I think the article is fairly succinct and well-written. To the extent people should become specialized is a concern.
The idea is striking a balance between specialists and polymaths. Polymaths can benefit for society as much as specialists can - as the shared examples of "combining two ideas to invent something new" shows. If you invent something new, people can specialize in that new field and improve upon it and build from it.
Both are equally valuable and equally self-serving as well as society-serving. It's what the individual values that matters the most.
I'm an autodidact and would consider myself a polymath, or at least interested in learning many fields well above a "generalized" level - but not quite at a specialists' level. A jack-of-all-trades approach.