Homework's largely supposed to be about reinforcing the lesson for math courses. For other courses it's largely about reading which shouldn't be done in class. Tests/essays are for assessment.
Other countries don't put as much emphasis on hw and seem to do just fine. In some of them hw isn't even graded, it's for you to practice. My high school for example gave out a book with the problem solutions. For some of them, it was only the final result, for some of them it was the whole process. Hw didn't affect your grade at all and it was up to you to decide if you want to do the hw or not.
The amount of hw students get in the us is astounding. It's not always productive either (more often that not it's not). And it seems like there's no pushback against it.
1. Homework should absolutely be graded to provide students with feedback, assess learning progress, and tailor instruction to strengths/weaknesses of students in the current iteration of the course. Once all the work goes into grading, it's hard for teachers to throw out that data when assigning grades.
2. It mimics the real world where sitting your butt in a chair and turning in useless reports is valued -- perhaps not as much as actual outcomes, but still valued. Perhaps that's stupid, but in most jobs it's a reality. IMO this isn't a great motivator, but it's one a lot of teachers cite.
3. Helps pad the grades of students who are terrible test takers / have anxiety issues.
4. Students are... students. They don't always know what's best for themselves. Making homework worth a portion of the grade communicates to students that they need to practice. Patronizing? Maybe. But also a reality.
5. It's the easiest way to inflate grades without explicitly lowering standards.
The amount of hw students get in the us is astounding. It's not always productive either (more often that not it's not). And it seems like there's no pushback against it.