The use of a rubric for grading essay questions in a new quiz is currently not very powerful.
I would like to suggest the following design changes for your consideration:
Our district would also love to see these changes made to the rubric style grading in New Quizzes.
We would use quizzes a lot more if you could grade each essay question with a separate rubric.
That is an excellent idea; however, just posting it in the forum will not result in any action. This idea may already be in the Idea Conversation area - you would have to search there to see if it is present and then upvote it.
If it is not present, then a new idea conversation needs to be started: