After making my request, a few cab companies simply answered "Ok" before hanging up. I called them back to get an ETA, and their dispatchers would give me answers like "30 to 40 minutes" or "I don't know".
I wasn't out in the boonies or anything. I was downtown.
Chicago did not have this, and when Uber offered UberTaxi it really was the best of both worlds, for a small surcharge on the normal cab fare.
Cab companies refusal to acknowledge this means they deserve to die. The economics are there, an app is undeniably cheaper, at some point, than a call center, and fundamentally whatever prices Americans pay to cab companies is clearly enough to sustain them, so it should in theory be enough to sustain an Uber-like company.
And let's not even get into the conversation about servicing more rural areas, where ZERO cab companies exist, but Uber drivers do. That is a net value add to those communities, no denying.
I used a small family taxi company. I had to book in advance, or be prepared for a short wait, but they understood my father in law needed some extra time and understood his requirements. Ubers on the other hand are awful with disabled people in my experience.