I am not saying the CC0 is a good license, I personally use CC-By, and for a very good reason: The CC0 undermines copyright, and all the other licenses by making them irrelevant, if CC0 is deemed legal. I mean how can anyone claim copying is unethical if the artist expressly permits copying without attribution? It is a paradox we don't want to see. The question "How do we question anyone for plagiarism if CC0 is legal?" comes to mind.

If you publish work X under CC0, it has no bearing on the copyrights that apply to any other works by you or anyone else. It does not undermine copyrights in any general sense. You can still release other works under any license you see fit.

As I said in an other post, I'm of the opinion that if someone tried to pass off works created by other people that are in the public domain as their own by explicitly saying so or allowing people to believe that, that would be unethical even if it were legal and did not violate any copyright laws.