Help me out here, and I'll warn in advance that I'm playing devil's advocate...

If Miers was White House counsel, doesn't that make her Bush's lawyer? If so, wouldn't any communication between them fall under lawyer-client privilege? Whereas executive privilege is a nebulous concept with no clear definition, lawyer-client privilege is a clearly defined legal concept: a lawyer cannot be compelled to testify about anything that has transpired between her and her client. So why all the executive privilege rigamarole when a better case for her not having to testify could be made based upon lawyer-client privilege? She could be compelled to appear, but she couldn't be forced to testify about anything she did on Bush's behalf. Or am I missing something?