High false negatives due to low viral load in samples would be problematic for diagnosis and treatment (except there is no specific treatment) but for
public health purpose it is just as important to test for infectiousness. Imagine if we have a quick and easy way to self test saliva with high false negative rate due to viral load in the saliva, we can feel more confident about not infecting others through talking even if we can't be sure we are disease free.
Roughly 1/3 covid tests are falsely negative[1]. I'm not sure any have been cleared/approved by the FDA yet, but some are authorized for emergency use due to the circumstances.
"Testing was performed using the cobas(R) SARS-CoV-2 test. This test was developed and its performance characteristics determined by LabCorp Laboratories. This test has not been FDA cleared or approved. This test has been authorized by FDA under an Emergency Use Authorization (EUA). This test is only authorized for the duration of time the declaration that circumstances exist justifying the authorization of the emergency use of in vitro diagnostic tests for detection of SARS-CoV-2 virus and/or diagnosis of COVID-19 infection under section 564(b)(1) of the Act, 21 U.S.C. 360bbb-3(b)(1), unless the authorization is terminated or revoked sooner."