I have to remind my Kinder to do her homework but I make it her responsibility to make sure her folder is in her backpack. She forgot one day and had to clip down a color (the horrors) and hasn't forgotten again. She's a pretty responsible little girl though who hates to disappoint anyone, so I say it depends on the child.
If they have homework they know it, and its their job to remember and do it.
Rule in my house is as soon as you walk through the door bags are opened and put on the table, they have a quick snack and get to work. Mostly they dont get homework only essays and special projects, but if they dont do their homework its their problem not mine.
My 10 yr old is bad for it (getting better) her teacher agrees 100% her responsability to take it out and do it. If it does not get done she looses recess and does it. But she gets homework 3 times a month. lol its just 30 min of reading a night is what they get.
But my 4 yr old comes home has her snack and starts reading her book from school while eating her snack and then does her questions and answers right away. Its routine routine routine. lol
She's in 4K and I don't really have to nag. Normally she wants to do her homework right after school at the Middle school where we pick up my SO's oldest son. (We have to sit there for 45 mins) but I'll prob. have to "nag" both of them until they graduate. I don't feel it's 100% just my children's responsibility though, but also the teachers and mine. School can be a drag and sometimes kids honestly forget they have homework from being caught up by something else. So it doesn't bother me one bit to nag them to do it. I kinda feel like not letting them do it, because they don't won't to, and making them get in trouble at school by the teacher makes you look like your not doing your job.