The Overall Taxi experience (or all of public trans for that matter) in Seoul is much, much better & cheaper than anywhere in the US. It's usually pretty easy to catch a cab, and when you can't you can get a "call taxi" and have it arrive in a Uber-esque time.
I'm not sure if anyone in Korea would pay the premiums that people pay in NYC/SF, especially if taxis get a comparable app.
Yeah, the taxi service in Seoul is among the best I've ever experienced (if you can get over the language barrier and sometimes grumpy drivers). Fast, cheap, ubiquitous. Several tiers of service, bullet taxis, company taxis, self-owned, deluxe.
For some tiers, drivers have to have 5-10 years of accident free driving - in Seoul that's remarkable.
Here's an example fare: $2.50 to pickup and go 2km, about $.70 a km after. Gangnam to Gyeongbokgung palace (across most of the city and over a major river) will run you about $15.
A trip from Brooklyn to Harlem, about the same distance and complexity, is likely to run $30-40. Uber will run you $40-50.
A big mac meal in Seoul runs about $6. I think the sandwich is about $4. I wouldn't know offhand since I've only ever eaten once at a McDonald's in Korea, and that was 8 years ago.
Something interesting that I found was that in different cities, the price proposition changes.
For example, in London, Black Cabs are generally considered decent but expensive, so Uber is priced cheaper than black cabs, but slightly more expensive than mini cabs.
In Delhi, the prices are far higher than anything you can hail on the street, but cheaper than calling a town car service.
I'm not sure if anyone in Korea would pay the premiums that people pay in NYC/SF, especially if taxis get a comparable app.