IMO, there are even bigger failures by the White House than the messaging failure. While that is important, no failure was more important for this country than the CDC failure in January and February. They refused testing assistance from the WHO, designed and shipped out a faulty and useless test, blocked private labs or institutions from conducting tests, and then created testing standards that made it impossible to test people for community spread. It was the fault of the CDC more than anyone else that the states were flying blind throughout February as the Virus took hold. By the time the first positive test came back in New York City, there were probably 10,000 people who already had it, and they were starting new chains in Boston, Los Angeles, New Orleans, Detroit, and Chicago, and those chains would feed the next set of outbreaks in the US.
Notably, the CDC is part of the executive branch, run under the White House. The CDC director, Chosen and nominated by the President, Redfield, is historically problematic, having pushed a so-called AIDS vaccine without evidence and who has worked with an abstinence-only education group. One senator in 2018 described him as " a sloppy scientist with a long history of scientific misconduct and an extreme religious agenda" which is the kind of thing that at the time might not have seemed like a big deal but then when the CDC became the most important organization in the country for a month...its performance mattered a lot.
The CDC was key to fighting 2 outbreaks during the Obama administration, Swine Flu and Ebola, and while it is possible to make some mistakes and learn from them every time, it is clear the CDC was completely broken when we needed them and tens of thousands of Americans are dead specifically because of that failure. This should be at the heart of whatever investigation is conducted after this is over.
Also along those lines, the administration allowed the FDA in March to begin approving all sorts of junk tests including specifically junk antibody tests that did not actually have any power to verify anything.
Furthermore, the administration was also sloppy with supplies. Elizabeth Warren had her plan for COVID response out on January 27th, calling for, among other things, increased production of PPE. That did not happen - in part because the White House had spent several years trying to privatize the effort. There needed to be early training of first responders for how to deal with infected patients. Didn't happen. There needed to be surge funding available to be working on these things in February. Didn't happen.
On top of all of that, consistent leadership from the top, supported by scientists, is also key to beating this, and the administration has been missing in action. For one example In South Korea, to reopen things, they developed a nationwide app system where people could log in, to aid in tracing. IF we wanted restaurants open right now, having people log in on an app as they enter the building is a way to make sure that if there is an infected individual recorded there, you can find all the other people who were potentially exposed and get them tested and isolated to break transmission chains. Amarillo Texas is not going to build its own app to do this. If there was a nationwide one? Everyone could use it. Does anyone know what we really need to do to reopen schools safely? NO. Why not? There is zero organization or leadership from the top. Under what circumstances should a state shut down fully a second time, is there any leadership from the top on these standards? No.
That's all in addition to the messaging failures, telling people it's a hoax and saying why they don't need to take precautions.