The registration is required in order to prevent the collecting societies from collecting royalties on your behalf.
Thank you for the explanation; that's quite different from what the EDRI-gram and Slashdot articles make it look like, and actually similar to what we have in a few other countries (maybe someone can mod you informative). Then the points I made in my earlier comment below become irrelevant in this case.
I'm opposed to the system of collecting societies too, but I'm also living with it, and I don't see that it makes much of a difference with respect to the creation and distribution of publicly licensed works. The members of the collecting societies get an unfair advantage, but the corresponding disadvantage is spread out in such a thin layer over the rest of us that hardly anyone notices.
While the option of registering your work to avoid having some collecting society earn money on it seems appealing, I doubt I'd ever take advantage over it, as that would help legitimize their way of doing business (much like I never "opt out" of receiving advertising I haven't asked for). I prefer to deny them those royalties they don't deserve by avoiding the distribution channels they control instead.