Unfortunately, my hosting site will rarely add anything that is not part of the core functionality of Moodle. I think that they cannot afford to support anything that has not been fully investigated by the Moodle community. So as these tools are not part of Moodle, they are not part of the Moodle they will provide.
Thank you for pointing out that what I want is possible. I look forward to the time when such tools are integrated into Moodle. My suggestion (to make it flexible) is that it should be possible to show a table summarising all the potentially submitted items. The tutor/teacher would then customise that table to show what was required for a particular application. The criteria (row/columns) might be date of submission, course, student, group, assignment, quiz, question, discussion, marker etc. Then the tutor on logging in would click on the cell/row/column requiring attention to go to the list for action. My need is to have a list in one place of all the quizzes and assignments that have been submitted and not marked, omitting everything else.