Historically in the U.S., "regulation" implied heavy-handed measures like rate setting, price controls, capacity setting, market segmentation, granting monopolies, etc. Scaling back those measures has been very successful. For example, deregulation of freight and airlines in the 1970's allowed the modern integrated delivery networks that make Amazon possible. The trend since then has been to avoid these particularly heavy-handed and market-distorting sorts of measures. I don't think even proponents of heavier banking regulations espouse regulating banks in the way we say regulated passenger railroads (which killed them).

In the context of cabs, a "lightly regulated" regime might require background checks, minimum insurance, and some sort of mechanism for verifying driver identity and reporting problems. Variables like rates, capacity, coverage area, etc, could be left to the market.

Deregulation didn't create the wealth gap. Government regulation favoring aligned interest (read: political donors) created a regulatory environment with sufficient holes and guarantees to allow this accumulation of wealth. Go look at the history of Congress, how many come out richer or become vastly richer afterward?

Deregulation does work in many industries, regulation should never be a barrier to entry into an industry but that is what it has evolved into. It is not there to keep the public safe, to ensure pricing, or even to maintain consistency of service, it is there to protect established interest and their political backers/beneficiaries.