Each of those options is perfectly fine for transportation if you planned and or intended to use them, what I mean is that whenever I've used a taxi or taxi-like service, car rental and/or public transportation would not have been a valid substitute or even possible.

Car rental because you have to pick up the car and later drop it off and the costs are significantly higher than a taxi, and public transportation because it's slower, more crowded (therefore more difficult with luggage) and doesn't always go directly where you want to go.

On a city-wide scale you can't expect car rentals and public transportation to be a valid replacement for a taxi/taxi-like service.

Have you been to Europe? I live in Poland and use public transportation as much as Uber - being able to afford both just as easily.

I have lived in Europe, although not Poland, but my point is not that public transportation is not useful, just that it's not always a suitable replacement for a taxi.