Soon, when you open up Uber and request a ride you'll see the pricing in a different way. Instead of its current method of displaying the rate (and multiplier, if surge pricing is in effect), with a fare estimate in a second screen, it will just display a guaranteed price to take you to your destination. Of course, that doesn't mean surge pricing is going away, just that it will already be figured in to the price you're quoted (with a "Fares are higher due to increased demand" note.)
Of course, if you need to make a change during the ride, either you or the driver can update it with a new destination, and immediately see what the new price will be. Also, the quoted price will still be in effect even if your driver gets lost or takes a different route. UberPool riders already see pricing this way, and Uber says it's been flipping the switch in some cities since April with hundreds of thousands of trips taken so far.
Miami, New Jersey, New York, Philadelphia, San Diego and Seattle are the first US cities where it's rolling out, and other areas should see it in the next few months. The only question now is if seeing the actual price up front will make riders more likely to use the service.