Let me start by stating my premise here:
Every parent wants to help their child succeed.
In the wake of college admission bribery scandals, the Harvard admissions case in which Asians feel they are being discriminated against, and the rising levels of student loan debt, the temptation is to regard the system as corrupt and rigged, rather than look for the ways in which it needs to be fixed.
1. Many people say that this shows there is not a level playing field. No, there's not.
As your parents probably told you, life isn't fair. My premise above means that in their desire to help their children succeed, some parents will clean motel rooms 10 hours a day so their child can get enough to eat, and graduate high school and attend community college. Other parents will be able to hire tutors and pay full freight for an Ivy League education. Let's face it. Rich people have more money. Rich people have more money they can use to help their children.
2. Getting into a top college isn't any guarantee of success.
In 2014, the economists Stacy Dale and Alan Krueger published an analysis of the benefits of attending a highly selective college. They found that, after statistically controlling for students’ SAT scores, economic background and college ambitions, the long-term financial returns are “generally indistinguishable from zero.” Students who are poised to succeed tend to do so even if they don’t get into the Ivy League.
But there was a crucial exception. There were strong benefits for the subset of black and Hispanic students, and for those whose parents had few educational credentials.
3. As the burden of college costs has shifted onto students paying for college with loans that extend for years afterwards, we have put a much bigger barrier to opportunity and social mobility than we have by letting rich people help their children.
It used to be that many state universities were essentially free. This was true of the University of California system until the late 1960s, and in 1975 tuition and fees were $600/year. https://www.abc10.com/article/news/local/what-happened-to-californias-free-tuition-a-history-of-fees-and-budget-issues/103-465128027
In my case, I went to the University of Missouri at St. Louis, where my total tuition and fees were $1250 -- in total for my 3.5 years there. Was UMSL a fine institution? No, but it worked for me, living at home and working part time.
I went to graduate school at the University of Michigan -- which was and is a premier institution. But I had financial aid from the National Science Foundation and also worked some as a teaching assistant and a research assistant. So, I got all the way through for my PhD with no debt.
You can't do that now; states have cut tuition support. The University of California is now about $12,000 a year. Even lowly UMSL is $350 a credit hour ($10,500/year, in-state)
This is a much bigger problem for a level playing field. Starting off with a degree and a huge load of debt, or not being able to attend at all, is definitely not a level playing field. This is a much bigger problem than the rich having better access.