Comment form won't appear in my theme
The "Comments block" module was the cause of this.  The module appears to be functioning as intended.  I just hadn't encountered this contributed module before, and didn't realize the project made use of it.

Because the "Comments block" module is installed, the "Comment form" block must be added to a region (e.g. "Content") in the theme.  This explains why the comment form was appearing in some themes but not in others.