There are probably a lot of different answers to your question(s), depending (among other things) on how your sections are created, how large your classes are, and what sector of education you're in (K-12, Higher Ed, Continuing Ed / Professional/Personal development).
I'm in higher ed (community college). All of our courses and sections are created via imports from our student information system. So every course starts with a section, and we cross-list (move a section to another course shell) for purposes of combining students. This is typically done for purposes of TEACHER workflow (build content once, have a single gradebook, etc.) but can also be for student experience (combine numerous low-enrollment courses to get more engagement in discussions, group assignments, etc.).
The use of groups is trickier, as you can have groups within a course, or account level groups. Your comment about "across all related courses" makes me think you're thinking at the higher level. At the course level, the groups are useful when students will be doing a lot of group work, not just one or two group assignments during the semester. And teachers have a pretty good window into what's happening in those groups.
I don't know if any of this is useful info, but maybe it will get the conversation rolling 
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