Japan, or at least the populated parts generally have tons of taxis so they are easy to find. They are polite and very clean, one thing western cabs are not. If they do something wrong (go the wrong way, end up taking the wrong road) more often than not they'll refund a portion of the fare without asking. I've had this happen a few times a year over the last 20 years.
Singapore is similar. Tons of cabs. In fact in Singapore you could book cabs in an app / online since like 2009. You get told the number of your cab so when lots of cabs are driving up you know yours is #27B-6. I had similarly nice experiences. I tried to tip a driver $3 for a $7 fare just so I could give him a $10 and he was like "too much lah!" and gave me $2 back.
I don't know how Uber is doing in Singapore but my understanding is not well. It's higher priced than local cabs for one.
My point being I agree with you. It's totally the taxis fault for providing sub-par service. In places where that's not the case Uber is having difficulty.
I suppose there's also the issue of car ownership though. For Uber to work you need people who own cars and are willing to drive them. Places like Tokyo and Singapore where most people don't own cars would probably make it harder to find drivers. I guess NYC has people from outside to drive in?