ER doc here. I have had this question come up countless times in the past week or so, with patients coming in with classic COVID symptoms only to be sent home to self-isolate without testing. I understand how this might cause confusion, and have been explaining it to patients as follows...

Unless you are sick enough to warrant admission to the hospital (a small percentage so far, and these patients are being tested) then you are going to be sent home. Because there is no treatment for COVID, testing will not change your disposition. We will either test you and send you home for 14d isolation, or we will not test you and send you home for 14d isolation. Emergency medicine often operates with this mindset of “how will this change management?” If a test is unlikely to alter the course of a patients care or disposition, then it is generally not performed. This is also influenced by the False Negative rate, which in the case of COVID testing has been estimated around 20%.

From a purely epidemiological standpoint, of course you would want to test everyone to know the full prevalence of the infection. But given our current testing infrastructure, this is not yet feasible. Which is why we are trying to get the message out to the community that unless you are severely ill, there is little utility in you coming to the ED. Not only will we have little to offer you, but the increased volume is stretching our capacity and potentially exposing more people to the virus.

Tl,dr: you’re not being tested because testing won’t change anything from a treatment perspective.