This article lays it out well. Basically, the issue is that we have hundreds of millions of people (both insured and uninsured) in this country who will hesitant to get tested for the virus because it could very likely cost them money personally. In countries with universal healthcare, this is not an issue. It is much easier to convince people in other systems that there will be no cost to them and that it is in their interest to get tested as soon as possible. In China, the government can simply say that no one can be charged for the testing. In Italy and South Korea, they have universal healthcare and it is free.
This is before you take into consideration things like paid sick leave, which the United States lacks and makes it far more likely that people will go to their work while sick and transmit it to everyone else. The United States is easily the worst positioned advanced economy to deal with a pandemic.
Cool story bro