Here's what I do...
I have two types of assessment. One is "assessment FOR learning" and the other is "assessment OF learning."
Suppose we're doing a math unit. There is ten assignments that are part of the unit. These assignments are graded, but the grades DO NOT count towards your report card mark. These assignments are to allow the student to chart their progress, and to identify their weak areas. The final Unit Exam (which can take many forms, I use projects and presentations mostly) is where the actual mark comes from, because now I assess your level of knowledge of the material.
As my student, if you choose NOT to do any of those ten assignments, well, that's up to you. It makes it tough for me to help you, but in high school, that's your decision. But, if you ace the Unit Assessment, then you get a great grade. You know the material, and whether or not you did the assignments is irrelevant. The assignments are designed to assist your learning and my ability to target your weak areas.
This is where most people chime in with "but at work" and other career related comments. School is NOT a job, it's not work, and I'm there to educated and test student's knowledge of the curriculum, not have them complete tasks. A job is often task oriented, learning something is results oriented. NOT the same thing, not at all. If companies want students "ready for the workworld" then they need to talk to parents and institute their own programs, because that's not my job.
Back to the no zeros. So, if you don't hand in the assignment, well, you just don't get anything. It's an empty box that I eventually mark "incomplete" so I know you didn't do it. Since your mark is the Unit Test, it makes no difference. Don't do the Unit Test? Well, then you're skipping a LOT of school. Only students that drop the class, or out of school, really manage to do that.
This type of grading is considered better for students. A student that is weak with the material initially, but learns it well is not penalized with some poor marks in early assignments. It allows students and teachers to find gaps without the pressure of marks. I love it.