So, even if there is hailing via an app (Which afaik exists for some black cabs), you're still paying the regulated and more expensive fare.
You get what you pay for.
The taxi business as we know it ought to die. Let these thieving, exploitive 'mogels' go bankrupt.
Then customers will cry out for regulation, insurance, etc. And it'll put the prices up.
I don't understand why you'd put your life completely in someone elses hands without any sort of vetting, regulation, insurance etc. Just so you can save a few $
Maybe a startup should disrupt the medical industry. Just provide "doctors" to patients based on online feedback scores. After all, all that regulation and training just pushes prices up.
There are numerous events of murder and rape in regulated taxi cabs. (Google is helpful). If you have any evidence that Uber is more dangerous than a cab is love to see it.
As for your final question, yes. Regulation has artificially held back the medical industry and ridiculously inflated prices. People aren't stupid, they can decide what's best for themselves. Choice and free competition is the foundation of progress.
Look at airbnb and the detrimental effects it has on cities. Residential areas are residential for a reason. It must be horrible to wake up one day and find that your neighbour has decided to turn into an unregulated hotel.
Secondly if the prior taxi system is evidence of regulation i think it's a safe assumption to make that regulations helped neither the consumer or the providers. Uber in SF is doing 3-4x what the entire taxi system was doing prior, that's evidence of demand not being met. Artificially restricting supply is never a good idea.
Uber is only doing so well because people prefer their service to the alternatives, people aren't stupid, they can do what is best for themselves.