For me still this equation holds true.
Taxes are abundant and cheap in Singapore. Riding in someone's car makes me uncomfortable. (But that is just me, I suppose)
The success of Uber in a city is directly proportional to how much taxis suck in that city.
So Singapore is one of a few cities where that's the case (NYC also -- Uber doesn't really work there. I was there for 8 days and requesting an Uber as a 10-15 minute wait. You can get into one of a million cabs that go by in that time. I gave up).
Same in Bangkok. Taxis are plentiful and cheap. But like elsewhere if you flag one down they often refuse you if you want to go somewhere inconvenient for them. That's where a taxi hailing app like GrabTaxi is useful. It works like Uber except it's a taxi that picks you up. Uber exists here but hasn't got much traction (as far as I know).
NYC is actually one of Uber's most important cities. Don't forget that NYC is more than just Manhattan below 125th street. Getting a taxi in the outer boroughs was miserable. The green ones help but were a little too late. The black car services are entirely unpredictable and unreliable, doubly so if you are not of the ethnicity of the dispatcher/drivers they employ.
And let's not even talk about the number of times a cab driver straight up refused to take me to Brooklyn, both during the day and late at night. Totally illegal, but it happens all the time.
Agreed, when I was living in the Valley in 2003/4 public transportation was terrible and taxis nowhere to be found.
But then I was driving a shitty Ford ....
That's not my experience in Singapore. The one time I was there I had to wait 15 minutes to get a taxi and then had to argue with them to get them to take me where I wanted.
In contrast, Uber took less time and required no negotiation.
Taxis are abundant and cheap in Shanghai... unless it's raining (very common). Then they won't pick you up at all. They're still driving around, but you can't actually get one.