If your symptoms are mild enough to not need hospitalization, your instructions are the same regardless of if it's the coronavirus, flu, or common cold. Now they're just telling the general population to follow those instructions.
What really disappoints me is that people seem to think it's okay to ignore those instructions if it's not the coronavirus. One possible silver lining to this mess is that flu cases will probably be significantly reduced in the short term.
Instead we're effectively doing the opposite, which is testing IF AND ONLY IF you BOTH have symptoms AND can prove contact with a confirmed case. Which doesn't do much to stop transmission (it's too late at this point; you've already spread it), and certainly doesn't give an accurate picture of the prevalence or behavior of the disease.
(EDIT: Found an article I saw the other day about this being done in an Italian town with the claim that the virus has been "eradicated" there as a consequence: https://www.theguardian.com/commentisfree/2020/mar/20/eradic...)
I'm just a lay observer of all this, not an authority. But my impression is that the U.S. could have done it effectively if a) the CDC test situation had not been borked and b) the federal govt had acknowledged the risk of epidemic (because I expect it's the CDC who has expertise in this tracing exercise, much more than state health departments).
As to whether it's too late, I honestly don't know. But it seems like it would be useful in controlling the epidemic regardless of its state.