South Korea could mass test because of how small it is, and because it has one of the best hospital and healthcare systems in the world. They are also a highly compact nation where testing labs are not very far from anywhere in the country; that is not the case in the US.
We do not have the time, resources, or public trust to waste on sampling/testing measures that are not fully vetted yet.
Delays cost lives yes, but how many more lives will be lost if tests aren't accurate and the public loses trust in the entire testing system?
I get wanting to do something, or have something, NOW. But rushing this sort of thing is likely to make the problems we face WORSE, not better, in the long run.