Even if they were able to be compared, all of those cities have congestion issues as well, many much worse, despite supposed "functional public transport" they have.
Which of course is a function of them having such large populations. Imagine how bad the congestion would be if their public transport was bad or non-existent? You are quite right that higher population density makes public transport more efficient and easier to provide.
As someone who uses public transport in Auckland every day - I no longer own a car, although I used to hate sitting in traffic when I was a daily driver - I can confirm our PT is more than functional.