I'm pretty sure the GP is suggesting the article doesn't provide a compelling reason why the dialect/language in the article should be preserved beyond just being a note in a book somewhere. There are tons of things which we keep a copy of, but for no more reason than just to remember it.
With regards to Chicagoese, maybe I was just listening to the wrong people, but I grew up in Milwaukee and went to Chicago basically whenever I wanted for most of my young adult life, and I never heard the term Chicagoese until reading this article. I actually thought the article was satire on first read, and I would agree with the GP that there isn't really a compelling argument for it, any more than I would suggest that we preserve the idiosyncrasies that my deep-woods Wisconsinite grandparents would come up with as I grew up, even if everyone in their region used the terms.
I really don't get the thrust of the article's argument other than being upset that Chicago was ranked the accent as unattractive in the YouGov survey.