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"Also, put yourself in the 1935 mindset - was there even auto insurances? were there seat belts? The risk profile people lived with was much different."Indeed, and that's precisely the start of much industry regulation. Not just taxis, but railways, boats, and all other forms of shared transport. Transportation safety was a Big Deal in the early 20th century, and the market did differentiate itself on that point - but there was also little regulation or oversight to ensure that claims of improved safety were actually real (see the most infamous example in the Titanic).
Mandated seat belts, car insurance, brake mechanisms (e.g., trains), speeds, inspections. All of these were borne out of necessity. The lack of safety in the 1935-life is why we are living with so many regulations today.
Our history seems to go: new technology, a lot of people are killed by new technology, regulation to improve safety of technology.
The "let's deregulate everything!" angle is just winding back the clock. To before the regulations became onerous and excessive, but also to before the regulations saved a lot of lives.