For medical purposes, you don't even need to test the sick. We don't have treatments available at this time, so the course of treatment doesn't current vary. IE, if you have COVID-like symptoms and are moved to the ICU, the course of treatment is the same with or without a positive test.

I've seen it argued that instead of testing the sick (as we currently do), we should be testing individuals who are "high touch" and likely to infect others (even lacking symptoms). Medical staff, first responders. Pharmacy and grocery employees. Bus drivers. Etc. I don't know enough to argue this is a better approach.