Earlier quoted context omitted.
The top universities (such as those in the Ivy League) typically give full financial aid to any admitted student who comes from a middle or lower class socioeconomic background. The "tuition problem" primarily exists at mediocre private universities (as well as those public universities that have significantly hiked tuition in recent years) which depend on squeezing every last penny from their students.
This is absolutely true and often shocks applicants that I meet in alumni interviews (although some know it well). Most of the Ivy League offers a full ride (as an official policy) for students who come from families with <$100k/year in income. This is not merit-based, it's need-based. It's a nasty misconception of "anti-elitists" that the Ivy League is only for the rich (although as others have pointed out there are…
80% of American households earn less than $100k and if 80% of the students got their education for free that wouldn't work out well for the universities.