Optional homework almost definitely won't get done. Making it count ensures that students would actually do it, which is useful to instructors (what do they need to focus on in class? Is the class understanding the lectures?).
Maybe that's the trick - make the requirements for passing good enough that the minimum still requires learning and engagement, and then just grade on a straight pass/fail.
Basically, perhaps construct a class like this
1) HW 20% of the grade
2) Quiz (say 1 Q a week related to homework that was returned a week ago, give students a chance to figure out what they did wrong) - say 20% of grade
3) midterm and final, a 30/30 or 20/40 split.
one can adjust the percentages to achieve one's desired pedagogical goals.
personally, I don't find copying homework to be a problem if the student figures out what they copied. It's no worse than students frantically copying down everything the teacher puts on the board or slides which seems to be a common way students study.
I never had quizzes except from professors who issued them to keep attendance up. Quizzes by nature are short and shallow. At the college level they are not particularly useful for establishing understanding.
While I believe "almost definitely" is a bit too strong, one of the most important lessons undergraduates need to learn asap is learning how to learn effectively. Homework is only a tool that can be very helpful when learning, but it's not the only tool available.
> which is useful to instructors
That's nice, but it's the instructor's job to serve serve the students.
> Is the class understanding the lectures?
In most classes, this should be easy to determine simply from interacting with the students in class, the questions they ask during office hours, etc.
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The ideal instructor should offer regular homework problems/projects that are clear examples of what the students will be expected to know, and check the work of anybody that wants to take advantage of the instructor's knowledge. However, if a student feels their time would be better spent elsewhere[1], that's their business.
The exam will reveal if they made a good decision. Like any skill, many students will make mistakes when they first attempt this kind of project/time management. Fortunately, as undergraduates, the consequences of failure are usually having to retake the class. Later in life, failure may mean losing a job or other far more damaging consequences.
(For the record, when I was an undergraduate at UC Davis, many classes had optional homework. I spent a lot of time working on it for some classes, and others I skipped because it was trivial compared to what I was doing every day at my job.)
[1] e.g. other classes, a job, their own self-study, or maintaining friendships at a social event
Then they fail?
I don't mean to sound glib, but I don't see the issue here.
Students that want to pass will pass, students that don't, won't.
I say this as a student that didn't pass.