Fine, but it doesn't work when one side plays by different rules than everyone else.

I agree. Abolish the medallion systems and other industry protectionist laws. Then cabs will just become a federated competitor to Uber and prices will fall to the same level, if not lower. I guarantee that the taxi lobby will not approve of that. They want government protection to revive their dead monopoly. There's nothing morally wrong with that; they're just looking out for their own interests. It's on the rest of us to see that for what it is.