I understand your complaint, but I don't really feel like it would be very feasible from a business perspective. Black cabs set their own prices. Uber trying to predict those prices is a lose-lose: anytime they underestimate the cost, users will be pissed they had to pay more than expected. Anytime they overestimate it, they risk the fact that some users who otherwise would have called a cab may decide to figure out another option due to high prices. Uber just isn't in the business of predicting cab prices, any more than a normal cab you hail on the street is.
Yes, in an ideal world, they would estimate the cab price. But in an ideal world, iPods would come preinstalled with music and plane tickets could be purchased 5 mins before the flight at the same price. But these things just don't make business sense. I have a strong hunch that the time and effort put in by Uber to predict prices would only marginally increase their revenue, and certainly wouldn't increase their profits.
I was under the impression that this was not the case with Uber- that they specifically reached out to black cab companies to partner with them and establish rates. I may be wrong, but it's a real shame if I am.
Ah interesting, looks like you're right, I wasn't aware of this (see pricing at https://www.uber.com/cities/san-francisco for example). However, all the fares are per-minute when travelling < 11mph and per-mile when travelling > 11mph. This means that a significant amount of prediction would still be necessary, with quite a bit of error on either side, so I think my points still mostly apply.
It does suck though, quite a few friends of mine were burned on new year's eve and are still a bit reluctant to do it again after that one expensive experience. One friend got hit with $200 for going half a mile... he cancelled the trip midway through when someone called him to cancel the cab, and got Uber to refund another $100 or so a few days later.