[ProblemFactory]

> How long before there's an uber-Uber that just sends your request to all the dispatch services and the first one that shows up gets your fare?

There already is an app for this, with over a billion existing users: Google Maps.

If you search for directions in London, there's a "ride hire" tab next to public transport. It gives you price estimates for Uber, London official taxis, and Hailo - all booked with a button from Google Maps, never having to open the Uber/Taxi/Hailo app.