The habit of correcting homework the first or last thing in class can perhaps explain some student delays or early departures. Assign just enough homework. Students' classroom habits depend on the teacher's classroom habits. Remember to assign a little bit of homework every class. Never less than one nor more than three exercises.
Students usually have much to do.
We don't want to overload them. Give them the choice. You can plan more than one type of homework and tell the students to choose the one they prefer, or you can ask them what they want to do for homework so they are free to choose their own home exercises. Better late than never. Do accept it when students bring late homework.