Wuhan's capabilities up until about two weeks ago were a max of two thousand tests a day. Even now, they are only able to test more patients because of horizontal scaling, aka building more machines to eliminate bottlenecks in the RT-PCR pipeline. The rest of the world is significantly behind. The test may also be run several times per person because there is evidence that there is a high false negative rate while patients are still asymptomatic.

There are so many people suspected of infection in just about every nation that there is simply not enough tests to go around to test people at random.