the wealthy can provide all kinds of advantages for their children (tutors, better schools, private schools, etc...) that are simply not accessible to poorer children.
Exactly. That tutoring teaches rich kids things that poor kids simply haven't had the resources to learn. These kids will continue to have tutoring and will continue to be better in school.
The rich have had more time to develop, more support that means they are less likely to die in an accident or due to degrading health or mental illness. They make a better investment overall, compared to those who are poor.
They had better schools.
Once you are at a college level, that is who you are. Yeah, it doesn't mean you are better than the poor kid innately, but you are now. You are the person who had that tutoring, and had that stability, and had those connections. That's what makes rich people better. It's not innate, it's because we invested more resources into them.
This is, of course, on average. There are awesome and competent poor people and stupid fucking wealthy people. that doesn't change the fact that the people born to stability and aid are generally better than the people who weren't.
In fact, the wealthy are significantly more likely to attend top schools, regardless of academic achievement
Yeah, because the top schools are horrendously expensive, because the "top" costs a lot of money. I'm not in a rich family, and if I were accepted into a top school I'd laugh my ass off, because I, and no other person with a normal life, can't afford that shit. Instead, I went to the school that gave me an all tuition paid scholarship.
Allowing poorer children easier access to higher education can help them escape poverty
Yeah, until the poor kids without a strong family with knowledge of the world get a bunch of bunk degrees and end up with shit educations and no jobs. Until those kids go back to a life of working at mcdonalds, but now with a psychology degree and a shit ton of student debt.
Until the value of degrees are driven down because now everyone can get them and none of the kids stand out by having a degree, and the rich kids just shrug it off and go get a masters before using their connections to get a job anyways.