I've been thinking of payments a critical component of Uber for a while now.
Because driving an illegal taxi is dangerous. You can get in trouble with the law, and you can get mugged. And if you get mugged there is not much you can do, because then you'll get in trouble with the law. In other words, Uber's main value proposition (to drivers) is safety from the law, and safety from the passenger.1
The first "safety" is easy: although driving for Uber is still mostly (and used to be almost always) illegal, I'd be shocked if Uber didn't somehow reimburse drivers for tickets they receive for operating an illegal limo service or cab.
The second one is tricker. How does Uber prevent passengers from mugging cab drivers? Because Uber drivers don't carry cash. They don't have to. Remember those bulletrpoof divisors yellow cabs used to have? They wouldn't have been there if cabbies never carried cash.
Often I hear people say something to the effect of "Uber is an example of how regulation kills innovation" or some similar regurtitated talking point. But I think this is missing the point. The real friction in innovation is the U.S.'s midcentury payments infrastructure.
I don't think that Uber's dispatch system is actually that important. In places with the highest density of uber pickups (outside bars at night, financial district in the morning, touristy places on the weekend), a gipsy cab driver would be able to pick up as many fares as an uber driver just by lowering their window and asking "hey, where are you going?"