For instance, many programming exercises in various subjects taught at my university give the students a basic framework with missing functions, or a test harness, or some other piece of code that needs to be finished. These could have been shared via a version control system, and delivery could be made that way as well (using pull requests, branches, or some other feature).

That way, students would be encouraged to use version control while working on the exercises.

The way it actually is done here, though, is basically "learn version control yourself and justify your choice of version control system in your report" when doing group projects.