Like here in Nottingham Uber doesn't support the suburbs 2 years after arrival. You can go there with Uber, just not come back, no-one's around.
A local app with better suburb support is ultimately going to win, as if you can only go one way, Uber becomes annoying.
How can Uber not support an area? If a both a driver and a passenger in Goldsport Wyoming both have their apps installed, they can't transact?
At least with other private hire firms you can phone them up and they'll be there in 10-20 minutes rather than just saying no drivers available.
Well, they're also being trained to use ridesharing generally. It's pretty low friction to move from Uber to Lyft or another competitor. Think of all the other entry points into that market, like Google or Apple Maps (or any other mapping company) for instance. Once autonomous transportation arrives it also moves from an opex to a capex problem, and that changes the barriers to entry, the headwinds to critical mass, and the competitive landscape significantly.
When I arrive in town I don't research which app to download and register with to get the best solution, I use the one that is the path of least resistence, that's firstly uber, secondly a local cab that's on the street or that the hotel will call for me.
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.