And then a large portion of drivers who only drive as a secondary or supplementary income don't drive, and there is a supply shortage, meaning prices surge.
Minimum wage is the acknowledgement that supply/demand is not sufficient for wage control. Your argument seems more like an argument against minimum wage in general.
You should tell that to the majoroty of (my Seattle) Lyft drivers that bought a Prius just so it could be their primary form of employment. From my personal experience it is only in the Bay Area that people use ride share as a supplemental income.
I've found that all of the Lyft drivers here (also Seattle) that start conversations drive as a side thing. I have no statistics, but it appears you don't either.