I'm not entirely sure how Taxi's work in big cities, from my interaction with them I think they work based on the idea that there's always going to be x number

I'm not entirely sure how Taxi's work in big cities, from my interaction with them I think they work based on the idea that there's always going to be x number of people in need of cabs in any area so driving around looking for patrons provides value to both people looking for a cab (cabs everywhere!) and value to the cabs (people everywhere!). If a company like Uber takes off and eventually the uber model is delivering 50% of taxi rides, won't that harm the traditional cab market (less patrons) and in turn harm the customer experience (harder to find a taxi wherever you are) therefore requiring people to use the uber model? For example right now you could get an Uber ride in an available city easily, or you could get a traditional cab. If Uber took 80% of the market wouldn't that force you to use Uber? Just thinking out loud and may be misunderstanding how it all works, but if my thinking is along the right lines it seems there are genuine downsides to the Uber model taking the largest market share beyond just "current taxi drivers will have to change how they work".