I'm surprised they still haven't. I gather that some cities have them, but one generic "summon a cab" app hasn't arisen. I suspect users would be just as happy getting a dedicated taxi rather than the somewhat hit-and-miss nonprofessional drivers.

They just want it to be simple and reliable. The taxi companies left that market open. I believe the success of ride sharing has less to do with the sharing, and more with the ease of being able to get a ride. I'm sure the cab companies would hate to give up whatever it is they imagine to be their differentiators, but users just want to get from point A to point B.

I did some searching and there are some already, but the network is so small and so weak compared to Lyft and Uber

And install a separate app for every car service