I'm guessing there is metadata originated on the "oops!" page that would differentiate missing file errors from other types of error screens, so Canvas would know which type of error messages to send to instructors and admins vs. errors to send to admins only.
Perhaps there could be a prompt on the error screen asking the student if they ran into a broken link, and give them an option to message the instructor directly (an of course send this error message to the Canvas admin as well).
Bottom line - broken links to deleted files is not a system error. It's a user error, and thus it's more important for the instructor to know about it than a Canvas admin.