@mclontz, as you indicate, that particular table is part of Classic Quizzes.
From the core Canvas perspective, a New Quiz is an external tool. Who is assigned something is controlled from the "Assign" block. Normally, that's done from the Assignment page. It's just that Classic Quizzes don't have a normal assignment page -- but it does have the assign block at the bottom.
Part of what Canvas was hoping to do with New Quizzes was to make it more of a traditional assignment than a quiz in the way it was handled. The New Quizzes doesn't have any extra information about who is supposed to take it because that's associated with the assignment, not with the quiz. That list likely won't be added to New Quizzes because it has nothing to do with New Quizzes.
What @james_whalley suggests will get you better information, just not in as succinct fashion. You also don't need to add /edit to the end of the assignment, you can get there by clicking. From my Quizzes page, I click on New Quiz and the assign block is at the bottom just like it is for other assignments. That same thing happens if I click on it from my Modules page or from the Assignments page. I'm not sure where the five clicks are coming in.
The assignments page actually tells you who the students are, rather than there just being 1 of them. At one time, I wrote code that would do look up the student names and let you see them, but I think Canvas has changed a lot since then I'm pretty sure it doesn't work anymore.
On the other hand, I try to avoid New Quizzes with a passion, only looking at them when someone has a question. I might be missing something.