I'm not sure how this is possible as afaik taxi fares are heavy regulated.
Just because Uber subsedises rides no city council will change the taxi fares.
"Taxi" taxis are not the only types of services like this. Depending on where in the world we're talking there have been other companies - often locally run or covering a few neighboring countries that use the same model Uber is using. Or offering similar ridesharing options via a phone since 1980s or 1990s.
In my area (Eastern Europe) Uber matched the prices of other unofficial "taxi" services that existed for 40+ years. However, the convenience of having an app, not dealing with cash, ability to see your driver getting to meet you, etc. boosted the number of taxi riders tenfold.
Many other ridesharing companies are offering apps these days, too. So even when Uber goes bust, the industry won't revert back to cash payments and phone numbers. So like the grandparent said it's a net positive for consumers.
A lot of places there is a sharp licensing distinction between requirements for those who want to be able to pick up unscheduled passengers on the street or taxi ranks, vs. those who only pick up on request or from their own locations. Overall the latter category tends to face far fewer limitations and be a lot more competitive.
https://www1.nyc.gov/site/tlc/passengers/taxi-fare.page
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