I'm sure Uber would tell you that's exactly how it's supposed to work. The price increase drives some people to seek alternate modes of transport, which keeps the supply stable so it's still possible to get a ride if you're willing to pay the higher fare.
Wellllll.... Their general line is not "surge pricing reduces demand," but "surge pricing increases supply." Clearly, over here in reality, it does both, but they prefer understandably to emphasize the up-side.
The question is, how much does it increase supply? My guess is that it doesn't increase it all that much. Uber does not, to my understanding, have a huge pool of irregular drivers who only occasionally go out onto the road during high surge pricing. They encourage their drivers to work full time, and most surge pricing (ie, not anomalous events like snowstorms) are at times of predictable high demand, when you'd expect most of their drivers to be on the road anyway.
My guess is that surge pricing (especially surge pricing in excess of x2) is mainly a windfall for Uber and their drivers, and is less effective about increasing supply than their promotional material would like you to believe.
Disclaimer: I work at Flywheel, an Uber competitor. I am not un-biased.
