Alas, I don't think people want to shop for a cab while hailing one. It is not a very efficient market. Cabs may come by, and you can look at their prices on the door, but are you really going to do this multiple times, hailing and rejecting taxis? The drivers won't be very interested in stopping for you to get rejected either.

Now in reality, people would learn the taxi brands in a competitive market, but even if they did are they going to sit there letting Brand X taxis go by in hope of getting a Brand Y taxi? How long will they wait.

Cell phone hail should not only get you the brand you want at the rate you've negotiated, but it should tell you how long it will take, and even let you consider other options, like paying more to get one sooner, or paying less and getting one later, as well as jitney options.

You do the shopping and negotiating not on a rainy streetcorner but at home, on the web, knowing not just price, but reputation and reviews and the works. That's an efficient market.

Zone maps are simple, but of course highly unfair for certain tasks and highly biased against short rides. If you give your location and destination, this allows pricing based on advanced computer street models which can understand the value of time over distance. (For example, regulated price taxis charge by the mile, so you are often better off on slow city streets compared to the fast highways you would be driving if you were behind the wheel. And in fact for the cab, the highway might well be better, even in gas used, but the driver is not able to set that price. Computer models could give you a price based on the most efficient route to your destination but let the driver go any way that makes sense.)