Sure, but let's say you as a consumer don't actually care about the brand of the ride platform and just want to get to your destination for some weight of speed and cost. Then it doesn't matter if there's only Uber or if there are 50 private taxi services in your area. Once someone fills gap with a meta-privte-ride service that just locates the closest and cheapest provider it's trivial for someone like Uber to be undercut by a local competitor.
How are you going to make a meta-ridesharing service? The only way to tell what Uber or Lyft drivers are available is through their apps, and it seems like it would be against their interests to do anything than make their communications as proprietary as possible. If you prevent users from weighing options you are better able to capture users exclusively.
