If your children are so smart they can surely do some reading and research of their own. That's what I did back in prehistoric times (1960s and early 1970s). In the subjects I enjoyed I was consistently ahead of the bulk of the class and occasionally of the teachers simply because I read all the text books and spent time in the library. It was enthusiasm that drove my performance not the imposition of extra homework.
“Although previous research has shown that homework improves students’ academic achievement, the majority of these studies use data on students’ homework time from retrospective questionnaires, which may be less accurate than time-diary data. We use data from the combined Child Development Supplement (CDS) and the Transition to Adulthood Survey (TA) of the Panel Study of Income Dynamics to explore the effects of time spent on homework while attending high school on two measures of academic achievement: high school GPA and college attendance by age 20. We find that homework time has no effect on these measures of academic achievement.”
Rønning, M. (2008). Who benefits from homework assignments? (Discussion Papers No. 566). Oslo, Norway: Statistics Norway, Research Department. Retrieved from https://eric.ed.gov/?id=EJ908287 Full text available http://www.ssb.no/a/publikasjoner/pdf/DP/dp566.pdf
I know many parents whose kids stayed up until 1-2am at least once a week. We expressed strong opinions to our kids that sleep is way more important than getting an extra grade bump, but many kids still trade sleep for a better grade.
/slight sarcasm.
US schools have changed, a lot, in the last 30 years. Many schools now are pressure cookers on both the teachers and peer levels. So some kids stay up very late and some go on antidepressants. On the other side are schools where no one cares about academics, and the bar for good grades is no mischief. Which is also not a great school for any kid.