@MatthewHammers ...
You have correctly identified the differences between adding a rubric to a graded assignment vs. adding a rubric to a graded quiz.
As you can see from both of these Guides, the process and location of where adding a rubric is different. And, as you've seen, the option to "Use this rubric for assignment grading" is not available for quizzes. The reason, I believe, for this is because quizzes typically use the points from the quiz questions rather than the points from the rubrics. In fact, there is no connection that I've seen between points on a quiz and points on a rubric. For example, if a student answers 8 questions correctly on a 10-question quiz, the attached rubric does not pick up on that score.
As maybe an extreme example, in my former role as a Canvas administrator in higher education, I had worked with a couple instructors over the years at the school where they had quizzes (let's say the questions totaled 50 points), but the rubrics they had wanted to include with the quiz had a different grand total (such as 40 points). So, you can see how this might be confusing to students thinking that they are answering a 50-point quiz, but then the rubric is only worth 40 points. So, what is the quiz actually worth? While I didn't always understand why some instructors wanted to attach a rubric to a quiz, I'm sure there were very valid reasons for the need to do so.
I hope this explains how things work with Classic Quizzes vs. Assignments in Canvas. Sing out if you have any other questions about this...thanks!