People have tried to challenge cab monopolies for decades without any success.

First of all, the OP was making a general point about the best way to go about challenging existing laws. Since the point is general, a counter example suffice, even if it differs from the specifics of the situation being discussed. If those specifics make a difference in the OP's point, the onus of outlining why they make a difference is on the OP. This is how logical reasoning works, but every. single. time. someone points out a counter example to a general statement, there is someone like who who comes and moves the goalpost by saying "oh yeah, because X is like Y", and we're all worse off because of this lack of debating etiquette.

Second, you would be wrong to trivialize the importance of expanding the offering in cabs. Uber will go into neighborhood where Taxis don't, they can also be substantially cheaper depending on the city and the specifics. Having access to a ride late at night can mean the difference between being raped or not raped for many people living in high crime neighborhood. In addition, Uber provides a livelihood for a large number of drivers. The taxis that it compete are generally renting their license from a large company who is collecting the monopoly rent.

It's not a matter of comparison, it's defending what's right.