If you go out of Germany you'll see that Germany is pretty unique in it's love for cash. Especially striking when you go north. The more north you go from Germany, the less cash there is, with plenty of places in say Sweden or Estonia where cash isn't even accepted. Thus suddenly having to have cash for a taxi is very jarring. (I don't even remember the last time I paid for anything in cash in Estonia. Definitely more than 10 years ago. On the flipside, every small city restaurant I visited in Germany in 2019 didn't accept cards.)
As for a ~30 second call resulting in a success story, that does sound pretty good indeed.
Let me tell you what my decades of taxi ordering experience in Estonia looks like. I call a taxi company [1], wait about a minute, nobody even picks up the phone. I try another company. I finally get someone to pick up, I tell them where I am, and they proceed to tell me that they have no taxis available. I have to call a new company. Eventually when the 5th company promises to send a taxi, there's a greater than 10% chance that they never show up. Sometimes I call the taxi company and they say the driver went on a break. Other times they say the driver picked up someone else on the way to my location. Sometimes the company has no clue whatsoever why the taxi didn't arrive.
With this old system, whenever I was in a rush, the most time-optimal plan was to run to the closest taxi stop and physically find a taxi.
The arrival of Uber & friends has mostly removed this nonsense. It's all so much more reliable. Although not 100%, sometimes when I'm ordering from a suburb, the driver will call me and ask if I'm willing to pay extra in cash for them to come out. If I say no, they cancel the order.
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[1] All these calls are to reasonably priced taxi companies, similar to Uber pricing. If I were willing to pay 3x price, there are plenty of premium taxi companies who will come and roll out the red carpet in exchange for your wallet.