Most taxi services will send a car to your address immediately, no reservation required. Problem is, you have to know the exact address where you want to be picked up, which can sometimes be difficult to determine if you're new in town and/or standing on a street with no obvious sign or address, e.g. on the edge of a large university campus. That's where GPS-driven apps really shine, plus the ability to see the car's location in near real-time, and why I will never be sad at the demise of traditional way of having to call a cab.
Indeed, but I was referring specifically to the charge that taxi alternatives (eg, outside the medallion system) existed pre-Uber. And I think, they did, but only in very limited use cases like airport shuttles, and not with fleets anywhere near large enough to have a car five minutes from anywhere at all times— hence the need to book those things ahead.