Everybody acknowledges that wealth is an advantage, but almost everyone also seems to underestimate the extent of that advantage.
It's very difficult for someone who has not actually lived it to fully appreciate the effects of chronic financial instability. Being middle class is generally regarded as "normal," so members of that class tend to take many aspects of their life for granted. The problems faced on a daily basis by people who have no financial resources outside of their own income from shitty minimum wage jobs are totally alien to them.
Imagine that you're working on finishing your bachelor's degree, and your only means of transportation is a junker that might break down at any moment. You know that if it ever needs any work more extensive than an oil change, you simply will not be able to afford it. Your parents are as broke as you, and won't be able to help you under any circumstances. Your access to both your $12/hour full-time job and your classes depends entirely on the continued functionality of that barely street-worthy bucket of rust.
Every day of the week, you wake up at 6:00 and work for 8+ hours. Right after work, you drive straight to campus for evening classes. You generally don't get home until around 10:00 PM, at which point you complete your homework as quickly as possible so that you can get at least a few hours of sleep. Your weekends (the ones you don't have to work) are set aside for papers, time-consuming reading assignments, and other major academic projects. You have literally no free time, and are constantly anxious about the possibility that your car will break down, or you'll lose your job, or you'll find yourself responsible for some other impossible expense--perhaps a stress-related health problem of some kind.
Your social life is nonexistent. Your teeth are covered in coffee stains because you don't have dental insurance and can't afford to have them cleaned. Your diet is nutritionally bankrupt--it consists almost entirely of instant noodles, frozen pot pies, and whatever happens to be stocked in the vending machine at work. You can't even imagine dating, because you barely have the time or money to take care of your own basic needs.
Compare that to the experience of someone who is living in an apartment rented by his parents, driving a car that was given to him as a birthday present back in high school, and paying for college with student loans that he was only able to take out because his parents were willing and able to co-sign. Doing well in college is hard, even for people who have the luxury of worrying about nothing other than their studies. It is orders of magnitude more difficult for those who truly start from nothing--no trust fund, no safety net, no rich uncle, nothing but a barely livable wage and a desire for a life that isn't characterized by constant struggle.
I know that probably sounds melodramatic, but that's the life many Americans lead. I've lived it myself, and am only just barely on the other side of it. The idea that every American has "equal" access to quality higher education is absolutely ridiculous.