Making it unviable for 80% or more of the drivers to benefit the 20% is a tradeoff that one doesn't have to make. There's nothing in the rulebook for creating regulation that says you have to be so heavy handed. All it shows us is that these are lazy regulators who didn't bother to write decent regulations.
This is all obviously assuming there's about a stable mix of minimum wage jobs available in the market to people who need them. Remember that this job needs a new car every few years so there's a bit of capital investment required to maintain this job. There are financing options available but now suddenly this minimum wage work is further costing you even more to pay the financing. Then you're left trying to address that.
Every legal change to the market can have unintended consequences and infinite imagined ones in advance. Some times it's better to just stick to simple tweaks/changes that have a pretty well trodden path of study by economists. It is also important for cities to explore different things too though so that we can collect the data but which city really wants to do that with its citizens, especially how hard it is to pass helpful reforms for which the market response is well-studied and the law easy to explain to people.
It was a guy who just started an insurance company with his wife and they were taking turns ubering when they could to help pay the bills until their company got off the ground.
It was a wife who was saving up for a kitchen remodel she wanted.
Several people who were retired.
Several people with waxing/waning medical issues.
In my experience there weren't a lot of people who were using uber/lyft for their long-term income, which make sense because the pay isn't very high, there aren't any promotions, and many of the individuals who would be interested in a that type of job don't have a nice enough car or have other issues that prevent them from driving for Uber.
As an extension, there is a utilitarian argument that says a full time driver will benefit substantially more from the minimum wage than a part time driver will suffer.
Regardless, I think appealing to the proportion of drivers is misplaced. It would be unsurprising to me if more than 80% of trips were completed by full time drivers.