The price would get so high that demand would plummet -- more shared/saver rides or public transit or own drive or flexcar/cargo carshare outside of the densest Urban cores.
I'm not sure about "plummet" at least until you get materially more expensive than taxis. But you're right that decreases in demand mean not only fewer fares but also a less viable service at the margins.
When I've looked, it's appeared as if Uber is only marginally viable around where my house is. Decrease the number of riders and I could imagine the number of drivers dropping further to the point where it's not really a usable service.
