There’s a middle ground between “no role in a child’s education” and sitting with a high school junior every night until he finishes his homework.
Where, exactly, a parent should come down in that middle ground really, really depends on the kid. The one responsibility all parents have is to keep enough of an eye on the situation to understand what is going on and what needs to be done.
If the kid wants good grades but is a mess at keeping organized, I think it behooves a parent to offer tons of support in the form of helping the child develop techniques to stay organized (assignment notebooks, calendars, bag-organizing, homework checks, checking their grades to make sure they aren’t getting overwhelmed). Hopefully, these strategies become more and more internalized and the parent’s involvement can become more detached, but these kids can backslide up until graduation: I think a parent ought to keep an eye on them and nudge them as needed.
If a kid wants to get good grades but struggles with over commitment, it’s reasonable for a parent to step in and say “you are being a lousy person. You can’t live up to all this, you have to chose”. Kids don’t always see the inevitable consequences, and watching them slowly meltdown and make themselves ill as they scramble to keep all the balls in the air is really not productive: they don’t learn, they just burnout and feel like failures (IME).
If a kid wants to get good grades but has trouble learning the way school is set up, I think a parent ought to help them find ways to learn: at younger levels, this may mean helping teach them themselves, at older grades it may be helping them find the resources they need (such as going in early or staying late to work with the teacher, or a class/good book on study skills). Again, I think it would be irresponsible for a parent to watch a kid struggle and struggle and struggle but never step in to help the kid or help the kid get help. This is especially true if you have the kind of kid who internalizes everything/blames everything on themselves (I am just so stupid!)
If a kid just doesn’t give a fuck about grades, I think it’s pretty reasonable to let the kid live with the consequences: summer school, repeating a grade, whatever. It’s not the end of the world, and the kid can decide from that if they care.
I do think a parent has a pretty strong responsibility to teach a child not to cheat: I mean, in the end their grades are their responsibility, but cheating is an ethical issue, and I think parents need to take an active role there. The natural consequences just aren’t severe enough to make the point. (rather like if you take a 4 year old back into the grocery store to return a candy bar and the clerk just pats them on the head, laughs it off, and lets them keep it. At times, that’s about how schools treat cheating.).