Personally, I feel far safer in an Uber/Lyft than a taxi. They are usually cars that are quite new, and the owners take pride in keeping them clean and driving more carefully. Sure, they don't know the city inside-out, but with decent GPS, they can get you pretty much anywhere and you can watch to make sure they aren't taking you the long way.
I know there have been some incidents of taxi drivers mobbing Ubers in BA, but I think the taxi drivers have a lot invested in spreading that story around like it's an everyday occurrence...the last taxi I took in BA, the driver mentioned it in a way that sounded like a warning to us. Not cool. But hey, fear works.
The system is changing, and it's better for the consumer. I do feel badly for the taxi drivers, because they are wired into a system that has traditionally taken care of the driver and the taxi company at the expense of the consumer. Countless times, I have experienced taxis that don't show up, dirty taxis, unhelpful and rude drivers, getting ripped off and being given the runaround in order to jack up prices. Never with Uber or Lyft, and I use them all the time. No wonder this industry was ripe for the taking!