If Uber says 5 minutes, it might be 7, or even possibly 15 if things go very, very wrong. Heck, if it's gonna be 15 you know this ahead of time because you can see the driver making wrong turns.
If you call a taxi service, and they say "15 minutes," it could be 30, 45, or 60. Maybe they're mussing with the truth, maybe they're outright lying. You don't know, and without the map showing the driver, you have no way of knowing.
A lot of modern taxi services have apps (often written by just a few big shops and contracted/branded out, but still). So you can start to get some of the same assurances from Taxis that you could get from Uber.
Also even before Uber/apps, I never had a problem with calling a Taxi and it not showing up within a few min, and I've lived a lot of places.
The first time was in 2012 because Microsoft was paying for it. It was from downtown Bellevue (so not an obscure place). I called them, they estimated 15 minutes, and it took them 40 minutes to show up. I'd never called a taxi before so I didn't realize this was normal; I called them back a few times to ask what was wrong, and they just said "soon!"
The second time was in 2015 in a country that didn't have Uber. They had an app. The app didn't work. They also didn't answer the phone. I tried multiple times, including an hour later after eating lunch. I gave up and spent 50 minutes walking home in ridiculous heat.
The third time was in 2016 because it was in a small town in the US that didn't have Uber. They did have an app. Their "app" displayed a phone number and told me to call it. That was the entire app. I called it, they estimated 30 minutes and showed up in 45 minutes, and they charged me $40 for a ten minute ride. Small town so I can understand the wait, but the price was definitely because they knew I had no other choice.
Meanwhile, I get annoyed when Ubers take longer than 5 minutes to show up because they take wrong turns.
I think it's definitely a matter of luck and location. Some places have horrible taxi services, some places have okay taxi services. Some places only have okay taxi services now because of competition from Uber. Ubers are still nearly always a huge margin better.
I guess you never tried to get a taxi in SF, then. Pre-Uber, attempting to hail one could leave you standing in the street for several tens of minutes, and calling a dispatcher would get you the universal estimate of 20 minutes, which in reality would be 40 minutes or more, assuming they actually showed up, which was a tossup.
