I'll just give you my personal reasons for assigning homework.
1. I teach English (literature and writing), and an obvious requirement of English class is reading. Students simply do not have enough time in class to reador for me to help them perfect their analytical and writing skills; so much of the reading must be done outside of the classroom. Admittedly, if most of my students chose to read on their own, I would not have to assign as much reading homework because reading is central to learning and analysis, and my students would already have a great deal of practice with it. Unfortunately, each year that I teach, the number of my students who choose to read as a hobby decreases.
2. I also assign homework because I want my students to practice skills that we have discussed in class. I do analyze all of my students' homework so that I know if they are learning or if they need help on specific aspects of a skill.
3. Finally, I assign homework because some of my students go to college and some go directly into the work force and for either path, most of my students will have some type of take-home work--whether it's homework in college or an employee having to bring home schematics or other job elements to study and perfect (my husband is in the Army, and he often has "homework" for his job). By teaching my students that learning is not confined to the classroom, I hope that they will be better prepared for whatever they choose to do after high school.
I do believe that some teachers assign "busy work" for homework, and I don't agree with teachers' not at least looking at their students' homework because that sends the message that there really was no point in a studentcompleting the work--how is he supposed to know if he is practicing whatever the skill is correctly if a teacher does not even look at his homework?