Regulation doesn't stop murder, theft nor rape. If it did we wouldn't have prisons.

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.