Hubert Horan has done an amazing teardown with his series, "Can Uber Ever Deliver?" But you don't need to be a transportation logistics expert (as he is) to see that there are no national or even regional cab companies. The reason is that, after a certain size, the business simply doesn't scale.

Arguably, smartphones, apps, and usage of the drivers' own cars have together reduced the administration costs, and thus raised the scale at which a provider can profitably operate. That interplay of factors hasn't been around for 100 years.

Although I've often speculated if you could have had an Uber-like service in the 80s, where you register with your credit card on file, and then call a number with a location to get an estimate pickup, and then they page a driver to get you, perhaps with an authentication code.