You can do that in the USA too. Generally, the cab will arrive - but in many cases it is not profitable for the driver to come out of their way to pick you up so sometimes they will not. The problem being that cab drivers are mostly independent contractors, and the cab dispatcher and government regulators don't have much ability to force them to do things that will lose money.
Uber and Lyft monitor both the driver and passenger. The driver is more confident that the passenger will be present when the driver arrives. The passenger can be more confident that the driver will in fact arrive and not pick up someone else along the way, never telling the dispatcher that they changed their mind.
The lack of trust between taxi driver and taxi passenger ruins phone call hails. Once in Austin, I called the dispatcher for a pickup, waited for 2 hours while calling every 15 minutes and being promised a ride in 10 minutes, eventually gave up and walked 5 blocks to a major intersection and immediately hailed a cab off the street.
Since taxi passengers can't guarantee they'll get picked up, a taxi passenger will sometimes call multiple companies or pick up a random cab from the street. Since taxi drivers can't guarantee the passenger will be there upon arrival, they will pick up any random person along the way.
Uber drivers will be more geographically distributed to match real-time demand due to their systems. In theory. As well, drivers will be more likely to operate where they live if demand is there. Again, in theory. Therefore, less costly to pick up people.
Cab drivers who drive out to drop someone off are very likely to hurry back to the dense parts where they can pick someone up. Uber is able to cover a large hailing area, so if cab has gone to the suburbs, they are more likely to be able to pick up a ride from the suburbs.
