Maybe the one where you flagged down a car on the street, but you could always call to book a taxi and those companies worked exactly like Uber — over the phone, because it was the pre–app era.
Not in my country they didn’t. Booking or no booking, taxis did whatever they wanted. More often than not your booked taxi just wouldn’t turn up and you wouldn’t know until well after you needed it.
Uber also gives you a price upfront, and that is the most you will pay (+ tip, if you feel like it). I don't remember pre-mobile phone taxi system that gave you a price upfront. They used to list the price per mile, and then it was up to you to figure out the distance and make sure the driver took a reasonably short route.
So no, the old taxi companies did NOT work "exactly like" Uber.
I've seen more than a few people on this forum assert that the old taxi system was/is comparable to Uber or somehow better. I even got some shit for referring to it as old, legacy, I forget the exact verbiage I used. But it is old, and it is worse. I get the price upfront, I can adjust the "class" of car I order if I'm going to the pharmacy alone or to a nice dinner. Calling ahead to preorder a taxi feels like calling to order a pizza over the phone at this point. If I called, would they even know how to handle it?
Obviously we live in a different era now where things are ordered by apps instead of websites or phone calls, but those used to be socially acceptable ways to order things.
For sure, I was there. But we also used to have to have the people on the phone read our order back to us to confirm it, now I've got a screen that does that automatically. I'm not at all nostalgic for the alternative.
The whole thing end-to-end is the ride service though. The interface is the differentiator that made Uber popular and forced traditional taxi providers to compete for once. There used to be tons of anecdotes about "the card reader being broken" in traditional taxis, because they dodged taxes by only accepting cash. Exposing the whole process through an app and handling your billing outside of the car made tactics like that less useful. Taxis thrived on hidden information games and obligation; Uber doesn't remove that entirely but the playing field is more level.
Quoted for truth. I still take taxis from time to time if there’s no wait at a taxi stand at an airport or building. I noticed in places like Las Vegas things seem better now, there’s flat rates and everyone has touchscreen payment terminals in the passenger area. I remember pre-Uber occasionally getting cab drivers that would take suboptimal routes like getting on the freeway to drive up the meter.
Also, Uber drivers tend to show up. It was always a crapshoot with regular cab drivers. I don't have experience with other car services, maybe they were better pre-Uber.
It depends on where you lived. NYC had a large number of "black car" livery services where you would call, arrange a ride, and typically get a price up front. It wasn't legal to hail them on the street, but in practice it was pretty common to hail a black car (a "gypsy cab") and negotiate a price up front. Source: I lived a few blocks north of Central Park and in Hamilton Heights before Uber was a thing and took gypsy cabs a couple of times a week.