The first thing you should do is a one-time backup and keep the mbz file in case something goes wrong.
The simplest action the teacher can do is deleting the assignment activities that take too much storage, once they're over and after having downloaded all the student submissions. Another way would be to reset the course at the end of the term in order to unenrol students and delete their submissions.
It's best if you can be with the teacher the first time he does it.
What you can also suggest is using an external repository for big files (such as Dropbox, OneDrive, Drive or Nextcloud) but this cannot work with assignments unfortunately. Another advantage of doing so is the easier update of documents (edit on PC -> cloud storage sync -> latest version on Moodle).
I also strongly recommand having some kind of article explaining why and how to prevent course inflation.
I wish there was a way to delete the uploaded files, not the activity. I would like to say to the teacher, go to the assignment activity xx and delete the uploaded files... If I say delete the assignment, that will meet with more resistance. If we do this, we will back the course up first, just in case.
Thank you Max, appreciate the response.
I agree, there lacks a feature to delete all submission in an assignment.
Reseting the course is the closest way to do that but it'll wipe all submissions in all assignments. One can't call that a surgical strike...