I'm not sure what America should do - Australia's honours system evolved out of the fact we are a Monarchy, and for us, it's appropriate. A Republic might make different decisions for perfectly valid reasons. But I do note that you do have some elements of a civil honors system already - the Presidential Medal of Freedom and the Presidential Citizens Medal.
I think our system is appropriate because it provides very clear, very real formal recognition of both heroism and other forms of service by civilians. I think America could probably find such a tradition worth having.
Actually, I think it should come from the American people, a private institution. Look how long it took our government to consider giving Purple Hearts to Hassan’s victims in Ft Hood. Work-related violence?