One of my undergraduate professors had a similar problem to the OP's in the above question, that is, that students would skip many minor low-point assignments in favor of studying for big exams, and the professor felt that not completing every single assignment resulted in a lower-quality learning experience even though a student's average still might be passing or even excellent.
The professor's solution was a policy that any student who failed to complete all assignments would be automatically assigned a zero for the course. That is, the student did not have an opportunity to accept a zero for the assignment that was not done - they would instead get an automatic F for the course. There was no requirement that each assignment be perfect, or even good - the requirement was that you had to at least attempt and turn something in for each assignment.
Are there any problems with this strategy from a pedagogical or ethics perspective? Obviously, some universities permit this and some do not, and the instructor in question did announce this policy in the syllabus at the beginning of the course, but I'm asking from a more general or best practices perspective. It seems to me that this is a non-optimal solution, more specifically one that is using an academic assessment system (grades/GPA) improperly as a behavioral management technique. That is, this strategy is similar/analogous to dropping a student's grade from a B to a C because they brought a weapon to class, or (in reverse) restricting a student from attending a campus dance because they did not demonstrate sufficient mastery of Boyle's Law (implementing a behavioral intervention when an academic one such as a lowered grade would have been more appropriate).
Is this a fair assessment of the situation, or is such a strategy a legitimate tool?
Obviously, the minimum level of effort required to constitute "completing" an assignment was vague and something I did not actually inquire into - one might wonder whether or not turning in a piece of paper with "I like pie, here is Boyle's Law, Boyle's Law is great, the answer to all of the questions on this assignment is THREE." would have sufficed (well, it would have been more than a blank page!). That also concerns me - whether or not being able to identify a boundary between making random guesses that effectively constitute not trying at all and an entirely incompetent, but sincere, attempt to complete the assignment (e.g. answers are all wrong, student failed to apply recent best practices covered in lecture, student confused Ohm's Law with Boyle's Law, student did not express all results to two significant figures as insisted upon in the instructions, answer was in French when English was required, student claimed that Cognitive-Behavioral Therapy was invented by Freud in 1543 and is generally considered effective in treating acute alcohol intoxication, student claimed that Orange is the New Black is a prime example of early twelfth-century Anglo-Saxon epic poetry, etc.), matters in determining whether or not such a penalty should be allowed.
This question has nothing to do with cheating or plagiarism.
Note: This was NOT Competency-Based Education (CBE). This was a regular engineering class that just happened to have this odd policy tacked on because the instructor was sick to death of students skipping his little 2 point assignments that he thought were critical. The course was otherwise entirely normal.
In response to @aeismail, yes, assignments could be turned in up until the date of the final exam, at least for purposes of not automatically failing the course for failing to turn something in.