I think it would be valuable for students to create their own Groups within an instructor created Group Set. They can name their Group something that makes sense to them. Also, this would avoid the instructor from having to create Groups one-by-one, which is tedious. Or, if the instructor chooses for Groups to be created automatically with the creation of the Group Set, it would avoid arbitrary Group names such as Group 1, Group 2, etc.
The biggest issue with the current structure is that students need to choose what already-created (by the instructor) Group they want to join. It requires an extra step of students who want to be in a Group together discussing what existing Group they need to sign up for, while hoping another group didn't sign up in that Group already.
Enabling students to create their own Group would avoid all of these issues and make the process of students signing up for Groups much easier.