Every article like this, there are comments like yours. Yet, I've taken a taxi many times, and nearly every time it was: call #, request taxi, "okay, 15 minutes", 15 minutes later taxi arrives, we drive to destination, pay by CC.
I've had a problem exactly once: I caught a taxi at the airport in Denver, CO, and like most airports, the pricing plan from the airport is different than to the airport (which is priced like a normal ride). Upon arrival at the destination, the cabbie didn't want to honor that agreement — "how would I make money if I charged that much?" — which, had I not been in shock from hearing about the stupidest remark I'd ever heard, I should have really told him exactly how he should make money.
But that was once, out of probably dozens of experiences. I've had far more trouble with, say, … airlines.
I've taken Lyft/Uber too, and honestly, it just isn't much different? The wait is about the same (relative to location, that is, less in crowded city centers). The difference is the ordering: with Lyft/Uber it is by app instead of by call. Slightly nicer, admittedly (can drop the pin, no need to understand often poor quality audio) but both apps absolutely murder cell batteries.