Cynical reply: Why don people mention it when the essay I end up grading is the best one they submitted all semester?
Considered reply: I doubt it. I lay a series of papers side by side and look over all of them before choosing one, and the one I choose is generally average or better. Besides, since you usually get three or more grades for written work, the effect will be less dramatic than you expect. In fact, only very rarely does such a misstep make a serious difference in one’s overall grade. You might submit an extra credit assignment or two, just to minimize the risk. And if you really think my system would penalize you unfairly, you can resubmit the body of your work at the end of the semester for me to look at in case your work is on the borderline between grades.