For accessibility reasons we are encouraging users to add captions and headers to their tables. However captions and headers are not always relevant, so while we should encourage their use, we should not be forcing users to use them. Looking at the WCAG, captions and headers are not mandatory (http://www.w3.org/TR/WCAG20-TECHS/H39.html and http://www.w3.org/TR/WCAG20-TECHS/H43.html) allowing for layout tables that, while we might frown upon them, are allowed and will be used by our users.
When creating a table you can add a caption, however there is no way to not add a caption to a table. The only way to remove a table caption is to edit the HTML of a table.
For headers, I think there should be a forth option for "Neither" so that users can have a table without header row or column.
For the caption, I think it should be possible to delete a caption row after the table is created using the context menu. During creation, if a user does not specify a caption, no caption should be added; alternately there could be an explicit control for captions, perhaps like the alt tag control.