It's the manual of STYLE not STANDARDS
The The Chicago Manual of Style editors:
many of us here ignore that rule, because it so often seems wrong.
Seems kinda strange hearing them say that, though later they also (properly) comment Readability trumps the rule, so the comma should stay. I've said before that the CMOS editors have a much more fluid relationship and commonsense approach with their manual than many of their readers.
This is from the November Q&A. Since there is no way to link to an individual month, here's the question.
Q. I’ve got a run-in list in which one of the items is a quoted question. The author put the comma after the closing quotation mark, which looks odd, but so does no comma at all. Any suggestions? The sentence: She can ask herself, “Why?”, formulate her own response, and see which option it closely matches.
A. Put the comma inside the quotation marks. Although Chicago style doesn’t call for the comma, many of us here ignore that rule, because it so often seems wrong.
My personal sordid and confusing relationship with the comma is not to be discussed.