The very best schools in the US: to choose a relatively uncontroversial list, MIT, Stanford, Harvard, Princeton, Yale -- all have need blind admissions, meaning they assess your ability to come whether or not you need financial aid. At least some (like Harvard) have sliding tuition scales that make the school totally free if family income is under $100k a year, or room and board only for family income under $200k a year, with some support continuing for families that make more than 200k.
Students want to go to these schools because they offer class mobility in the states alongside the excellent education.
Additionally you have to go well down the list of top tier universities and colleges in America before you get to one that spends less than tuition on its students. Yale states they spend about $90k over tuition per undergraduate for instance.