Parents can make a small short run difference through massive effort, if they really want to. It just doesn’t matter in the end.
What you can make a long term difference in is how fondly your children remember their childhood, if their parents were there, loved them, and were happy, rather than tired, stressed and angry.
The parental success being hereditary is not merely random, it is because parents put a lot of effort into making sure kids do end up the same. Intervening when things go wrong is one of ways how it happens. Changing school when peers or teachers are bad is also how it happens. If you don't care and kid don't care and you are fine with it, the kid will grow up into person that don't care when when left on own devices.
The tutor makes difference when preparing for tests that decide which school you go to. You being yourself when you actually finished the degree and you being yourself when you did not is not the same for jobs that require degree. In many jobs and societies, credentials, the degree and school and network do matter. Which is why those with resource push for those credentials.
When you don't know high school math well, you will have hard time in those STEM classes that require difficult math. They are difficult enough for students from good schools, those from bad schools were literally drawning. It makes difference between finishing it and having access to those jobs and not finishing it and not having that access. I don't know how in your school, but ours kicked a lot of people out on these.
You know who is in worst economic situation in USA right now? Students who did not managed to finish college, but do have debt.
It just so happens that parents in those situations deal with them, often by moving kids elsewhere or by having to spend a lot of extra effort and money to overcome that. When you have good teacher, the extra effort and money are just not needed.
Tutors exist for a reason and yes they make difference. Some schools produce kids that are on average good at later math, other schools produce kids that just don't (same city, same socioeconic background, different leadership). Somehow one city is strong in producing young programmers while other is not.
> Greg Clark’s work on social class persistence suggests that’s wasted effort. The heritability of social class is 0.7 in every society with records amenable to tracking lineages across generations, from Sweden, England, China, Korea and many other places.
The inequality as difference between poor and rich in USA right now is getting bigger. The middle class is lowering its numbers. The society is just not the same as it used to and is not actually reproducing the exact same classes.
I did had friends from weaker schools that struggled academically in college. They needed a lot of extra tutoring and help to overcome that. Some did overcomed it, so no they were not stupid and yes it evened out, but they had it much harder and had limited options on choice of major.
The worst off were those whose high school was too easy and were shocked by the system that required them to study hard things and study a lot. Yes, some parents will avoid those schools like a plague and cluster kids in different schools. It is not because they are all stupid.