One of the things homework specifically does not do is teach children to work by themselves without constant supervision. It cannot because homework is typically monitored and enforced. It doesn't really teach delayed gratification either and you have bigger problems if you're relying on homework to do that, even if it did work.
Depends on the kid really. My parents never checked or helped with my homework, even in primary school. As long as my grades stayed top shelf and I never got in trouble they stayed off my back as far as school was concerned. I was better off being left to my own devices. They noticed and acted accordingly.