You wouldn't go to ER, even as a positive test, unless you needed intensive care. Most cases could be isolated at home.
If you have a mild case of Coronavirus and are able to self-isolate, then just do it. Testing and confirming you have it doesn't change things, you'd still be asked to self-isolate.
I can see the value in people who are very sick - confirming they have the virus can inform the need for isolation in the hospital.
It might also be useful to have a diagnosis to present to an impatient boss who wants you back at work.
That's what my employer is doing now. If you're sick, work from home for 2 weeks. Don't come in.