The best question is not to ask what something doesn't treat, but to address what it does treat. The list of things a particular med doesn't treat is a very large list which I could not complete.
Therefore, I'm changing your question to: What does copper treat?. Sorry for this.
Copper has different ionic forms, the +1 and +2 being the most common.
Although it is known to kill certain pathogens and microbes, it is not necessarily the treatment. 0.6 ppm is on the high end of the scale for marine fishes. It is best to maintain a 0.3 to 0.5 ppm concentration. With certain medications, such as Cupramine, it has been shown to be quite effective down to 0.25 ppm when measured on the proper home test kit for copper. The lower the level the better it is for the fish.
The group of microbes affected most by copper include:
algae (blue green)
bacteria (e.g. those that cause fin rot)
fungus (some Branchiomyces sp.)
external protozoans
monogenetic trematodes
snails
ectoparasitic worms
some crustacea
As a poison, it should not be used unless one of the conditions require its use. For instance, look at the above list. If my fish has fin rot I don't treat with copper. I would treat with an antibiotic. Although copper is a potential choice, it stresses the fish, it's toxic to the fish, and shortens the fish's lifespan. The antibiotic treatment doesn't.
Each of the above has its specific levels/concentrations of effectiveness. Each requires either a certain time exposure (since quite often copper doesn't affect pathogens that are under the skin of the fish, yet they are still considered 'external.'), or a high concentration bath. Some require alternating high-low concentration applications. But they have one thing in common: Each treatment harms the fish.
Copper remains with the fish for quite some time, even after treatment, and its use is banned for food fishes for that reason.
Even at very high concentrations (e.g. >500 ppm) copper will not kill Myxosoma sp.
So what is left off of that list? Intestinal and internal pathogens. The external pathogens and parasites that fall into the pod categories. The external pathogens that are not considered to be protozoans (a few dozen of these at the least). And the list goes on.
It's common advantage is the killer of ciliated marine protozoan parasites of frequently seen diseases (Marine Velvet and Marine Ich). Nothing has been found to be as thorough nor as fast. Yet, this treatment does not totally kill all the parasites while they are on the fish -- only during its other life cycle stages.
So copper is used to kill the free swimming and cyst stages of protozoans at low concentrations -- regardless of the location of the parasite on or in the fish. This means that copper at low concentrations does not have a high enough kill ratio for those protozoans and parasites that can transmit fish-to-fish and which don't have life stages in the open water.
Work has been performed by me and other on high dip concentrations, alternating high-low concentrations, etc., but none have been 100% successful to totally removing the pathogen before the fish has shortened its lifespan to a few days or weeks. Cases of 'the disease is gone, but the patient is dead.' abounds in this area.