Those are a good example of the elected officials in charge being unclear on the concept.
Chicago is a huge city that was almost entirely platted and subdivided between 1840 and 1920, on a flat undistinguished plain. The result is a gridiron pattern unmatched anywhere else on the planet. Streets were wide (66 feet) and blocks almost uniformly 330-by-660 feet. (A city ordinance still prescribes this pattern, despite conflicting with modern city planning practice.)
While convenient and efficient, such a street layout was a mixed blessing as auto ownership and traffic grew. By the 1930s, developers and city planners eschewed gridiron layouts for residential areas, seeing how they encouraged speeding and “cut-through traffic.” Although outlying parts of Chicago still had many uncontrolled intersections (no signs at all) into the 1980s, other neighborhoods were plagued not only with speeding motorists but also drive-by shootings.
In the early 1990s, traffic engineers across the country were looking for geometric ways to enforce “traffic calming” that would slow and discourage traffic on residential streets. The toolbox included speed bumps, speed humps, chicanes, four-way stops, diverters that divide intersections into two right angles, cul-de-sacs, and mini-roundabouts. Chicago Mayor Richard M. Daley pushed for such measures across the city to make residents happy, offering the dubious evidence that the few neighborhoods with cul-de-sacs also had low crime rates.
Meanwhile, for cultural and political reasons beyond our scope today, Chicago’s elected aldermen have near-total control over infrastructure and city services in their wards, and any change even to one-way patterns or stop signs requires their consent and a city ordinance. When residents complain about speeding cars, one of the few things an alderman can do is to have a stop sign installed. If that's not good enough, they'll install a four-way stop—traffic engineering "warrants" methodology be damned.
So even as the city’s “downtown” traffic engineering professionals were offering a menu of fixes like mini-roundabouts, aldermen were reluctant to anger ward residents by removing the preexisting stop signs or one-way street designations. (In one case that I recall somewhere near Monroe and Oakley, a traffic signal was retained even after a mini-roundabout was installed.) Some aldermen went all-in on traffic calming, notably Ginger Rugai in the 19th Ward (Beverly area) while others didn’t pursue any changes.
American reaction to modern roundabouts has been strong—every motorist thinks he’s a traffic engineer—but some states (Colorado and Wisconsin) have installed them extensively on roadways controlled by the state. Some cities, notably Carmel, Indiana, have also gone for them in a big way. Old-fashioned, much larger diameter traffic circles and rotaries are common on the East Coast, particularly in Washington, Boston area, and New Jersey, and those often have traffic signals or stop signs controlling entry to them. Given the very local control over streets in the US, undoubtedly there are other places where roundabouts are accompanied by stop signs, but they’re not as commonplace as the Chicago examples.