I don´t know how is it in all of the world, but in many countries/cities, the problem with Taxi drivers is that there is no control, they treat you like shit, there is no one else to complain, they take you to the longest route, many have their "clocks" (that is what we call the machine they use to charge you the fare) fixed so that they charge more, and there are illegal taxis that steal from you (as in real robbery). Uber is good because you can complain to Uber, you get refunds, if drivers get bad ratings they are no longer part of Uber, and in general, it is safer than taxis. I was some days ago in another country. I didn't know any Taxi phone number, but I had my uber app, so I just requested an uberx, and it came. Problem solved.

It sounds like you'd be happy with a premium service (like Uber originally was). You pay more than a taxi but you get all the other benefits you list. Problem solved.

Taxi´s companies have existed for a while. Compared to Uber the differences are: customer support is shitty, good luck getting a refund, you need to know the phone numbers or have the apps installed of all of the cities in the world. It is more complicated. Uber is uber internationally. It is only one app, only one (relatively good) support. By the way, I don´t "love" Uber, is just that I see the value on it.