The other element of the situation is that people use litigation and politics to protect existing bargains. Cabs are regulated, for various reasons. Cities use them as an extension of their public transit infrastructure, and impose restrictions like requiring them to service the whole city, instead of just the profitable neighborhoods. In return, the cab companies are given a monopoly.
So if the cities allow Uber to skim off all the premium business, without requiring Uber to serve the sketchy/marginal neighborhoods, then that's the city going back on its side of the bargain. The cabs can't "win on merit" when they're playing with one hand tied behind their back.
The fair thing to do is either enforce the existing monopoly and keep out Uber, or alternatively to get rid of the monopoly and the regulations too.