This is actually an interesting idea. What if the city of SF created an Uber/Lyft-like app, and required that all registered taxis be listed on it and have the driver app running and active on their phone while on duty? Obviously taxis could still accept manual street-side hails and line up in hotel taxi lines if/when they want to. But they otherwise could accept fares on the app, and riders could still pay seamlessly through the app, and have the option to rate drivers and submit feedback.
They wouldn't be able to charge the rock-bottom prices Uber and Lyft do in order to gain market share, of course. But with Uber (and to a much smaller extent Lyft) suffering some backlash wrt their business practices and tendency to increase traffic congestion, such an app might have a chance at pulling at least some market share back toward traditional taxis.
If I could order a taxi using an Uber/Lyft-like experience[0], and get decent wait times, I wouldn't mind spending more in order to support a local alternative, if that local alternative was actually showing signs that it wanted to innovate and adopt a customer-first attitude.
[0] Yes, I know Uber had UberTAXI for a while, but in practice the wait times were huge and most of the times I checked the option, it said there were no taxis available at all. Obviously Uber had little incentive to make the taxi part of their service attractive, and plenty of incentive to make it unattractive, so I don't really blame the taxi services themselves for this deficiency.