I'm not quite as flexible as you; my rule is that you can turn it in late (with no penalty) until the day that I return the graded work (which I will delay upon request). I put in this restriction only to avoid the big pile of late papers at the end of the term, which seems to be less of a hassle for you than it is for me. I get similar results.

And yet, there are always a few students who just do not grasp how it works. I get ‘I'm sorry that I missed class yesterday; can I still turn the assignment in today?’ a lot. So ‘obviously fictitious due dates’ is sadly an exaggeration.