NYC is big. Really big (like space). It can support a number of wannabes. But you need a certain number of drivers to be able to serve users and the value of Uber is in the areas where you can't support half a dozen wannabes.
For example, I was in Australia recently and discovered that not even Lyft works there (in Perth anyway). This is in a city approaching 2M population and is very much a developed nation (well, except for the Internet).
Think about that: that's a ton of people who are being trained to use Uber. When they travel do you think they're going to pick up whatever the local ride-hailing wannabe app is for some specific city? No.
Uber has a whole bunch of problems but it's clearly a valuable brand at this point.