China didn't know what it was dealing with, how to assess it, or who to test. It did the legwork on all of that, for which the rest of the world should be grateful.
Test-kit availability has been constrained throughout the epidemic, and yes, that means that full confirmation has been only partial and lags outbreaks. But information I've seen is that once China was aware of what it was dealing with, it was testing as broadly as it could.
South Korea seem to be taking this even further, with many thousands of tests within a few days in outbreak areas. The US CDC have refused doctors' requests to test suspected patients and control the availability and use of test kits. That's simply fucking insane and stupid. (Again: the UC Davis Medical Center instance: https://health.ucdavis.edu/health-news/contenthub/novel-coro...)
Amateur hour is over.