Second it is not fair or decent to pay teachers based on performance, it is even foolish and idiotic to do it in that manner. Good teachers will leave inner city and under performing schools with a lot of literacy problems and low desire for eduction for jobs that pay a lot more in "good schools".
Third we need to keep children in their area where they grew up if at all possible, competing for students is not the way forward IMHO.
And the kids in South Korea may be doing well in academic tests, but almost 10% of children there contemplate killing themselves due to the extreme pressure put on them for academic success. South Korea is the suicide capital of the world.
Kids in the US have a lot of other things to keep them interested and many grow up to be reasonably well balanced and happy adults instead of over achieving suicidal mental cases like Asian countries seem to suffer from.