As a university level instructor, we still give homework and it's still a big part of the student's grades. It's still up to the student to decide if that's enough, but accountability is there. The students do not tend to ask themselves if they understand the material until they are in their later years of schooling.

I strongly dislike dealing with more homework so I tend to spot check and count participation in the exercise. Realizing that I only have three classes and not many students per class, I don't know how K-12 can possibly handle homework in any way but purely participation. They tend to have hundreds of students split among ~6 classes a day to deal with.