I live in a mid-sized city in the US. Before Uber and Lyft, if I wanted to get a ride, I had to call into a central number (sometimes with a 5-10 minute hold) and then had to schedule a ride. IF someone was available right away, it would typically take 30 minutes for them to arrive - and it's not uncommon for them to simply never show up. The cars are not Mercedes, but your regular utilitarian cabs. What you are describing sounds great, but is far from the norm in the world.

I don't mind cash but I rarely have it on me.