NYC has definitely always had a taxi "habit" despite their transit. I think London is similar. On the other hand Tokyo (which has one of the best transit systems) has lots if taxis as well, but I guess Über hasn't had much traction compared to local taxis (they've always been clean and offered good service).
About 3 years ago I've had issues multiple times in Tokyo with taxi drivers not speaking english at all, thus not being able to communicate the destination. I assume Uber would smooth over that aspect as there is literally no need for communication.
I don't doubt that, but foreigners who don't speak some Japanese is a real small percentage of the people who use taxi services. If this were a general problem, then I think Über would likely do better in a place like Tokyo.
Uber is not allowed to compete in Tokyo. When you use Uber, it just calls a normal licensed taxi. The advantage is presumably the fact that it shows your destination to the driver without you having to explain it, but for locals there's literally no advantage.