Some replies randomly listed. (Sorry, too tired to be diligent about quoting right now.)
Someone mentioned summers, and EFC (if not those exact letters).
At D’s Ivy, our expected family contribution was 500/yr.
She had to contribute by working a part-time campus job – a limited number of hours per week, which she did gladly for the fine education. Different positions as an underclassman, a position in her field as an upperclassman. That position worked handily into her eventual after-graduation job because she could claim experience. And the latter in turn gave her a significant edge getting into another Ivy for grad school. Given such a pathway (again), she was not complaining about having to work, nor was I. I also believe that, while she was always a good time manager, having small part-time jobs at a demanding academic institution, while still keeping up her extracurriculars, was really good life experience for her and also gave her confidence in nailing her first job after graduation, which she was offered 2 months after she finished her senior year.
Also, her school had a routine for FA students where they would sit them down at the beginning of each academic year and “adjust” their package to meet new needs, and they would also make adjustments during the year. That is, if she ran out of money for whatever reason, they simply gave her more. I’m not making that up.
The reality with low-SES kids is the travel (and yes, the books – someone mentioned). The time factor of travel, too, by the way, if it cuts into the part-time job or consumes a lot of time, such as at Thanksgiving if it’s coast to coast. There were several times when she could not afford to come home. She was fortunate that she was invited by classmates to their homes in the East. One summer I could not afford a ticket for her, nor could she. It was very difficult for the family. Ditto for some Thanksgivings – an expensive time to travel.
On the question of “majority” students “wanting diversity.” Yes, but it depends on what you mean by the word. For my D, it meant that she didn’t want a duplication of the imbalance she would have experienced at her state flagship, but it also meant that she wanted to meet * international* undergraduates, which she did at an Ivy and would not at her public. Almost by definition (not quite, but close), public universities are less nationally diverse and certainly less globally diverse on the undergraduate level. She had plenty of exposure to both URM’s and low-SES throughout her childhood, but broader exposure she did not have.
Finally, regarding any claim that if a college just becomes “diverse enough” (quantitatively), social integration among races will just “happen” due to greater visibility, that is quite naive. I am well acquainted with institutions that are 50-50, yet self-segregation persists in the 21st century – whether that’s whites + "ORM’s’ or URM’s + non-URM’s.
It is not about “numbers.”