Public domain is special since its a natural aspect of copyright law rather than a license, where a person don't need permission once a work is in public domain.

CC0 tries to mimic this but here the tricky part of permissions comes into place. If I give you permission to do anything and you remove the permission text and claim the work as your own, do you still have permission? It a rather popular discussion in regard to cc0, and the consensus where I have seen it seems to be that you need the license in order to have permission. I have also seen lawyers arguing that copyright law itself has limits on what rights a license can give, such as attribution.