These parents most definitely exist. They tend to be poor and disinterested in normal parental duties. If you don't have any interaction with them they may as well not exist to you.
Parents who think it is their responsibility to educate their kids and see the public school as one of the ways to provide that education will do things like show up for parent-teacher conferences, make sure their kids complete their homework, understand what their kids are struggling with, and seek out additional help when it is needed (asking the teacher, using internet resources, etc.). I'm sure there are some teachers who would say that describes everyone in their class, but most of the teachers I've talked to say that such a classroom sounds like a wonderful dream.
> There are parents who just aren't capable of taking a more active role in educating their own children
If someone who didn't graduate adopted a high school age student, then I would see your point. However, kids don't start out in high school. They start out much younger. While I'm sure you can find some very unusual exceptions, a parent should be able to take an active role in their kid's education from the beginning. Maybe by the time the kid gets into high school, some parents aren't going to be able to fully understand the math their kids are doing, but you can still take responsibility for what your kid's education even if you don't fully understand their calculus homework.
[1] https://nces.ed.gov/surveys/international/reports/2014-piaac..., definition of 'below level 2' at https://nces.ed.gov/surveys/piaac/litproficiencylevel.asp
And maybe it's wishful thinking on my part, but I think the situation is more subtle: There are parents who just aren't capable of taking a more active role in educating their own children and supervising their public schools. They have no idea what a good education looks like, or what their kids are missing out on. They don't have the time or resources to be "involved" in their kids' schools. In short, they have no realistic hope to offer their kids.
And the schools themselves aren't set up to be fully self sufficient without the supervision of "involved" parents (euphemism for "pushy", I'm one of them) and a supply of children who come to school ready to learn.
Might they believe that the government owes them the best possible education anyway? Sure. I believe that too, even though I'm one of those parents who has taken an active role in educating my own kids.
So I think the government is responsible, but as a last resort, not as the best possible arrangement.