If a driver ever asked this of me I would give them a bad rating along with an explanation. I'd expect the driver to get canned pretty quickly if passengers report such behavior and passenger reputation to be restored if the drivers gave them 1-star ratings. As far as I understand it, driver reputation is far more important than passenger reputation (they certainly have a lot more to lose).
Like the drivers who won't ask but will still give you a low rating if you don't offer a tip. And then you have the ones in the middle, who have tip jars sitting in the middle of their car. Source: http://www.huffingtonpost.com/entry/uber-driver-complaints-e...
Also, while you or I might complain, a lot of people are either too scared to speak up or just figure that a big company like Uber won't care, so this kind of stuff just goes unreported.
That doesn't happen with Lyft: because tipping is built into the app, nobody asks for cash.
I don't carry cash, so I'd be screwed if I rode Uber and a driver threatened me with a 1-star rating if I didn't fork over cash.