What if teachers didn't give zeros?
I don't.
Zeros are not an option. I've had rosters as large as 112 students and as small as 48. If you don't know me, I teach English language arts in the US public school system.
I adopted this philosophy 10 years ago and haven't given up on it.
Here's the idea:
Students (children) learn early on that it is easier to give up and take the "goose egg" than persevere through the task. They rely on extra credit or the next assignment to take up the slack.
If we allow that, they never learn. If we let them avoid responsibility, they never learn the skill. If they never develop the writing skill, they will not be successful. So, if I assign it, they must do it. If they do the work, they get paid. If they don't do the work they get fired, i.e. repeat the class.
Writing is a process so if they do not process, they never learn to write. When they get a job in the real world, if they can't write, they get fired because they don't have the skill to meet the deadline.
So in an effort to make productive citizens, I make sure they leave my class with the skills they need, not the ones they already have.
It's a little more work for me, but it's worth it.