Before Uber, the taxi company I used had an automated system which send a taxi to my place if I pressed 1, and connected me to human that took a new address when I pressed 2. Even with a human in the loop, it rarely took more than 40 seconds. I agree that Uber app is more convenient than that, but it really wasn't an order of magnitude improvement -- what was a deal maker for me was the fact that Uber automatically charged me, and I didn't have to put a card in and input PIN, or scramble for cash.