Blaming parents is a big excuse teachers started using in the 70's. However the great success of public schools was based on the ability to teach poor immigrant children in NYC. Their parents didn't even speak English. Schools became the great enculturating force, and they taught the children everything about how to be Americans. School was seen as the way up and out. Those children who have weak homes are the ones who need good schools the most. However, they need strong academics, not just free lunches.
What you say there would seem hard to argue against. Probably we are slightly skewed on observing each others points of view.
However, I paid a lot of attention to what went on in school as my children grew up, and regardless of what anyone says, teachers or otherwise, there's no doubt in my mind that the parents who didn't seem to give a damn had the kids that did badly academically. I'm going to say here that the immigrant parents of the past, and likely the present, probably gave very much of a damn and likely pushed their kids pretty hard in many cases.
But I jumped into this conversation by stating that the problem with public schools is that they don't have much in the way of academic standards anymore, which is what I still think. Of course, also their adoption of political correctness as an MO.
I would add, vis a vis the discussion on homeschooling, that the same parents who participate actively in their childrens' education in public schools are the ones who'd make good homeschoolers - the ones who don't probably wouldn't or couldn't.