I literally described my experience of booking a taxi before Uber. Many of the local services also had apps that showed the location of the car and a fixed price before Uber was available here.
Booking a courtesy car is different to most instances of getting a taxi, though. Getting a taxi is far more often things like "going to the line of taxis outside the club and negotiating prices with them" or "I landed in a foreign country on a business trip or family visit and I need a taxi to my hotel, and I don't have a local credit card". Before Uber, these things were far, far worse on average than they are now.