having been both a TA and a student, i think this idea is entirely too optimistic. "optional" problem sets can work well in graduate and advance undergraduate courses, but for the bulk of students in the intro/intermediate courses, homework that doesn't get graded for accuracy may as well not exist. i certainly didn't do it, and when the CS department decided to grade homework on completion only, i saw student attendance of my office hours immediately drop to zero.

ultimately, you cannot just expect college students to make reasoned decisions based on the way you set up the course. you need to arrange the course in a way that incentivizes them to keep up at every step.