Copyright doesn't apply to ideas. It applies to works, which are specific, complete expressions of ideas.

The problem artists have with LLMs is not that they routinely output copyrighted works (it can happen, but isn't common), but that they copy human-expressed knowledge and art styles on an industrial scale, thus destroying revenue streams that supported or encouraged creative expression in the past. I doubt this is going to be solved via existing copyright laws. I suspect that the need for disclosure of copyright on the source material is to build a case for more novel legal protections for artists down the line.