Homework is a way to encourage both student and parent participation
Students learn in a myriad of ways, and many use homework to prove their participation instead of in-person commentary. Restricting all children to the singular form of in-class contributions can alienate many. Parents, too, can use this time to participate in their child's education.
Homework teaches skills like self-disciplining and allows students to put in effort outside of class. Many students face participation anxiety or require extra time to process information. Homework allows them to practice. In addition, homework is also extremely helpful as preparatory materials for reviewing and tests. Here, especially under parental guidance, children can continue to review and learn outside of class without increasing anxiety around participation. Parental figures can be great teaching aids once they become familiar with the student's learning process. This allows parents who cannot participate in school associations and activities to still be helping their children.
Students who struggle with class participation should work on improving that skill rather than finding an unrelated method (like homework) to make up for it.