Sure, Stanford, Harvard & many top tier universities provide financial aid. I think that's awesome and to be encouraged. Getting into those institutions or being even aware of them is another matter. The disadvantages that many American's face start way downstream in high school, etc.

If you don't have parents who have gone to college before or go to a school with good teachers, you probably won't even know to apply to a top tier school.

A common theme that I have seen amongst my friends who have gone to Stanford/Berkeley/etc is that their parents had them doing extracurricular activities from a very young age to pad their entrance letters. Poorer families, have less resources and hence less time to engage in activities like this.

Just getting into Stanford or a top US college requires an incredible amount of work above and beyond good grades.

I have a very good friend who charge's $200 an hour to put together college application letters for top schools.

Income inequality in the USA is a huge disadvantage that many Americans face.

I'm not saying that income inequality is not an issue many immigrants don't face. I'm just particularly aware of it coming from a country (Ireland) that has good social benefits, like free healthcare, educations, etc. I think these things put me at an advantage compared to what many of my American peers had to go through.