All of that is very true.
Parents always have been, by far, the biggest indicator in the likely outcomes to a child's life. My wife used to teach in some terrible, sink estate state schools and was always the first person to suggest to A* pupils that college and university were possibilities. I think I'm staying the right side of data protection if I tell you that one kid she taught got a scholarship to an Ivy League university when his parents weren't even considering college. She bumped into a friend of his a few years later and found out he was working, fixing pavements. "Because that's what his dad does and he never needed university"
But even the perfect measures to fix that are, by their nature, a generation away from taking effect. They also need to be combined with some joined up thinking and departmental cooperation (

) on benefit reform.
Solving the parental issues would go most of the way to sorting the behavioural ones. Some of it can be dealt with by making the curriculum more relevant to those kids too though. That's where the grammar school system worked so well. Those suited to an academic education got one, without disruption from those more suited to learning trades and skills that would benefit their likely career paths. Those teachers who were freed from the pressures of academic education could spend more time focusing on behaviour management.
But the politics of envy will always make such improvement impossible. For the last three decades the focus has been on providing equality by dragging down the top, rather than just giving each child the best education possible and ignoring comparisons.