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.