Forgive me for not knowing all the details, but what is the extortion in the fact that Taxi co's have to pay fees that Uber and Lyft don't? I'm guessing there is more to this than I know.
If you feel that use of the streets is not being rationed efficiently, or that heavy users of the streets are not paying enough relative to light users, then you can impose some kind of sliding scale or conditional tax on street use. This is not at all the same as an absolute cap on supply.
not that i'm a huge fan of unfettered capitalism, but just clarifying...