Copying music costs the artist nothing.
That's arguable. Despite what some people think, there is the concept of a lost sale involved. I don't believe RIAA claims (which are no doubt very inflated), but when a song is copied many many times, there will be some percentage of people who copied that music who would have bought it otherwise. That might be a very low percentage, but it is assuredly non-zero. Also, there is the cost of lost control. Copyright law entitles the rights holder of an artistic pattern to the control of that pattern. Because they created it, they get the say in what happens to it. Just because the creation is digital now, does not automatically negate that. In a nutshell, copying a file may be easy and it may seem ok, but it's still illegal unless you have permission to do that. That's the cost for not having created it yourself or having secured the rights to it for yourself.
What we are learning is that once you release something that can be easily replicated by a computer over the internet, that thing is no longer just yours. The world has changed; you need to adjust.
The adjustment here is part of the argument in question. Just because the pattern being copied is easily manipulated, does not automatically mean it is morally acceptable to copy it. Copying it may be easy, but the fact remains that in so doing, you're using a template to create a new file. The template wasn't free to create, and the current system recognizes that by stating that the pattern itself has some value and that the pattern has an assigned ownership (which isn't you in this case). It therefore remains the property of the copyright holder. In effect, whoever went to the trouble of creating the pattern owns it, and they should be compensated for it.
The argument that the internet has changed the morality of these things is infantile. The difficulty of an act does not determine whether it is right or wrong. For example, killing someone with a bat would take considerable effort, and would be wrong. However pushing that same person off a bridge to their death is much easier, would cost almost no effort, and yet is still wrong. I'm not comparing murder to the unlawful copying of music, just illustrating that an eased effort of an act does not erase the morality of that act.