While you throw "applies at all income levels" into your comment---the fact remains that children whose families are low income are far less likely to receive a good education in our country than there middle class or above counter parts---which indicates that there are many more factors, or that schools can go a long way towards helping parents be ore involved, or filling the the gaps when parents cannot or will not (and at low incomes, can not is often the case).
I think things like helping parents get GEDs is meant to address this a bit.
You know, I have seen many low income parents who love their kids and want only the very best for them and want to be engaged more, but they have to work 2 jobs just to keep their kids housed and fed so, yeah, they are not around as much to be engaged because their income level makes that virtually impossible. I've seen parents who want to read with their kids every night but the only library within walking/public transit distance (if there is one at all) is not open outside of their work hours.
Heck, I have BEEN the immigrant parent who so very much wants to help their kid with their homework but cannot understand it because my language skills were not there, and I didn't knw what was expected from homework/projects in this culture to guide my child, and even the math symbols were not totally the same. It is a horribly demoralizing feeling to not be bale to do the basic parenting thing of helping your child figure out their homework when they need it. We were lucky to have the funds for tutors who could help (which, schools could also provide so kids whose parents lack those funds and similarly lack that ability to engage with their kids about their school work still get help),
So, yeah, sure, to whatever extent possible getting parents in and involved is great---so long as it is not used as an excuse to do less for other kids, or a reason to disrespect the ways that parents contribute to their children and families even when it does not directly correlate with schools.