We have a few of these here in Brazil (i.e. http://www.99taxis.com/). The apps work just fine, it's the taxis that lack quality in their service. Cars are usually beaten down, dirty. Drivers are impolite, almost never use Waze or some other GPS app and the fare at night rivals Uber's.

There has been some drama regarding Uber v. Taxi around here as well (São Paulo, Brazil). One thing I know for sure is that as long as Uber's around I'll never call a taxi again.

Yes there are apps that work with existing taxi services.

https://www.hailoapp.com/

Hailo was quite popular in Montreal for a while until Uber launched and drove them out of business. As far as i recall they shut down all of their North American operations to focus on EU. Wonder how that's going. I quite liked them, but I prefer UberX any day

Though Hailo is notable for recently having withdrawn from the North American market. Mytaxi.com is still around though.

>> Has any taxi service, in any city, rolled out a self-dispatching app for end-users?

Do you mean an app where an end-user can request a cab, or do you mean an app allowing you to become a cab?

If the former then there are at least two I know of in my small-ish south-coast city in the UK. And one in Perth, Australia.

If the latter, no idea.

For the record that's West Quay Cars and Radio Taxis in Southampton, UK and Swan Taxis in Perth.

I'm pretty sure there are now companies selling OEM taxi apps to taxi firms, ready for deployment after some integration and rebranding.

Flywheel in SF is in use by all the cab companies I think. Same features as uber (hail from the app, pay with your phone, etc) but only for the taxis. One cool feature is that if you get in a cab off the street without the app you can pull up the app while riding and they figure out which taxi you're in and you can pay via the app automatically.

http://www.seattleyellowcab.com/ appears to have. I've not used it (or Yellow Cab), so I can't give more information.