I think this means that if lawyers use it, they have also lost confidentiality. That could be a significant issue in a big case.
[Edit: Or maybe not, legally. But they have definitely lost confidentiality in the "corporate secrets" sense, and that may still matter.]
This is really the question. Conversely, why would an attorney get to have privilege over chatbot interactions in a manner that an individual using a chatbot for self-defense not have such privilege?
If lawyers use it, they may have the ability to claim work product exemption, although this itself is going to be dependent on a lot more factors I can't analyze.