Thanks for your detailed background analysis and exhaustive response.
See, for a teacher coming over to Moodle Assignments from the world of paper, the natural expected behaviour is "the due date is the due date - they are no late submissions". Late submissions are allowed in an instructor dependent manner in many Universities (including our own) but they then contain other possible fancy stuff like - penalty based on how late the submission is (late by 5 minutes is different from late by 1 day).
I think that allowing late submissions should not be the default as it is highly dangerous for some teacher who does not read all the docs and makes semantic assumptions on the basis of what is written.
In my case, I realized that the submissions were open a week after the deadline as I had just assumed that the due date was the due date. Imagine the sinking feeling I had when I realized that the submissions were still effectively open.
Should the cut off date exist as a control - absolutely. There are use cases where this would be useful (time dependent penalties where I can write an expression for a function with values between 0 and 1 which multiplies the score received would be amazing). My argument is about default behaviour.