There were multiple issues with testing, including bureaucratic and others. Doctors want to test, but they need stuff that works, that's reliable, and they're sure they're using properly otherwise they'll understandably resist it. They also need the full support of government, which, at least initially, they didn't get.
E.g.
"Jeff Duchin, the public health chief in King County, Wash., where 37 deaths have been reported, suggested the lack of tests was critical, in addition to the fact that authorities had limited who could be tested. Initially, they had said tests would only be used for those who had traveled in affected regions of the globe or had otherwise been in contact with an infected person.
“So, you know, if we had the ability to test earlier, I’m sure we would have identified patients earlier in the community, possibly at hospitals, but we were also looking at not only availability of testing but whether patients met criteria for testing,” Duchin said.” So, given the fact that we just recently acquired our availability of testing and new criteria were published, this person was brought to our attention.”
...
"Thomas Frieden, an infectious disease physician who served as CDC director under former president Barack Obama, called on Sunday for an “independent group” to investigate what went wrong with the CDC’s testing process. He said in the past, the CDC moved quickly to produce tests for diseases such as H1N1, or swine flu.
“We were able to get test kits out fast,” Frieden said on CNN. “Something went wrong here. We have to find out why so we can prevent that in the future.”
Frieden said the agency has been muzzled under President Trump..."
https://www.washingtonpost.com/business/2020/03/16/cdc-who-coronavirus-tests/
Time to catch up.