We are going to need to massively scale up that testing; per capita tests is not a terribly relevant metric. The best measure is: can we test everybody who needs it?
All around the country, many (most?) people with symptoms are being denied any form of testing. We need to go beyond that to massive testing of even asymptomatic people that have come into contact with people who have tested positive.
The healthcare workers are thinking about how to best help the people under their care, with severely limited resources. And for them, testing doesn't matter unless it changes treatment. But there are other reasons to test.
What the rest of our leaders need to be thinning is how to engage a strategy to contain the broader spread and let people return to normal life, safely, as soon as possible.
South Korea has shown us one way, massive testing:
"According to Gov. Cuomo [0] New York is now testing more per capita than any place else including China or South Korea"
No - this is not accurate. Both your statement and the statement by Cuomo are not true.
As of last Wednesday, S Korea has done 295 000 people, of ~50M. [1]
As of yesterday, NY has done 45,437 tests for ~20M people.
So Cuomo's statement is looking a little Trumpish, I'm not accusing him of lying, but he's spreading false information which happens to make him look good, he needs to be more accurate.
Also - your statement misinterprets his - the NYC statement says 'any other state' - not 'any other place'. Canada is testing a little bit more widespread than NY, surely there are others.
So NYC is acting, but there's no 'cutting edge' or 'exceptional' response in America of anything right now. S. Korea, Taiwan, Singapore are looking like 'world leaders' here, granted, they have different kinds of systems entirely.
It's possible that some of their other social artifacts, such as 'basic face masks' might actually be responsible for reducing spread. Since 'lockdown' in North America the spread has continued unabated, and in S. Korea, there's no lock-down and they have it under control (though they are doing more testing as well).
There might possibly be something very specific about the spread of the virus that we don't understand, which if we were to be able to focus on, we could be more effective.
2. This comment [1] illuminates a bit the point about not getting tested by your healthcare provider.
[0] Around 11:30 https://www.ny1.com/nyc/all-boroughs/coronavirus-blog/2020/0...
[1] https://www.reddit.com/r/nyc/comments/fmb6p5/just_had_a_sobe...