> tested in that case if you were seeking medical care because it was pretty bad, or the tests were encouraged by a contact tracing regime. The first part would lead towards higher positivity results, and the second towards lower.

That, in a nutshell, is the reason positivity rate matters.

If a positivity rate is too high, that may indicate that the state is only testing the sickest patients who seek medical attention, and is not casting a wide enough net to know how much of the virus is spreading within its communities. A low rate of positivity in testing data can be seen as a sign that a state has sufficient testing capacity for the size of their outbreak and is testing enough of its population to make informed decisions about reopening. https://coronavirus.jhu.edu/testing/testing-positivity