You miss one very important part of the history of the yellow cab company in Chicago: It succeeded as a business almost entirely because it had a state-granted monopoly. Although the article you cite doesn’t quite make it clear what Hertz actually started in the first place was a livery service not what we would think of as a taxi service. (Why else would it talk about response time if it was picking people up on the street?) During the notoriously corrupt 1920s, when most of the Chicago City Council was literally in the mob’s pocket–the company Hertz sold his business to lobbied the city council to pass a law allowing for the establishment of taxi-service-as-we-know (fare regulated) it and granting the company that bought out Hertz a near-monopoly on its operation.
It’s possible that things could have evolved differently if Chicago hadn’t acted as it did but the company he founded ended up building its business model on a state-granted monopoly with heavy regulation, not branding. That’s what made Yellow Cab a success around the country. In 1947, the Supreme Court ruled (probably correctly on the law and Constitution) that this monopoly wasn’t sufficiently related to the interstate commerce to violate the Sherman Antitrust Act. But nobody really disputes the idea that Yellow cab just clouted its way to the top. (Here’s something from the Institute for Justice with some of the history I’ve just described.)
This doesn’t mean that the market doesn’t respond effectively. Some cities–New York and London come to mind–heavily regulate and ration taxi service while letting livery services operate with minimal regulation. The result is that its almost impossible to get taxis in either city during rush hour, outside of office districts, and away from airports. On the other hand, both have plenty of inexpensive, pretty good livery services.