There's an argument that more competition could reduce prices and/or wait times for consumers, but there's also the argument it'll take away gig jobs, which are already somewhat of a "backup net" for people who need money but can't find a formal job for some other reason.
I don't live in SF anymore. When I did and now that I occasionally visit, I personally don't see any meaningful difference from when only Lyft and Uber operated there.
I remember once playing ball all day in the front yard, calling all the taxi companies just on a lark. They'd claim they were sending a driver, that the driver pulled up and honked, but we were outside the entire time. No one ever actually drove up over about 20 calls to 6 cab companies.
Uber/Lyft finally served all neighborhoods mostly equally, and that was a huge benefit.