Many of the really good ones have the same policy - I know Harvard definitely does.
Consider Harvard, MIT's, and NU's endowments. I attend Northeastern, where the CS college is excellent, particularly the opportunities to do research with programming language rockstars like Matthias Felleisen (The Little Schemer) and Olin Shivers (best known for his SCSH acknowledgements page).
The educational caliber of a school doesn't necessarily translate to deep pockets.
Massachusetts Institute of Technology | $7.982 billion (US dollars) Harvard University | $25.66 billion (US dollars) Northeastern University | $486.9 million (US dollars) (2009 estimates)
Harvard has 52 times more money than NU.
http://www.wolframalpha.com/input/?i=endowment+of+MIT%2C+Har...
edit: I keep expecting HN comments to turn _foo_ into italics.
The cost of attendance for all of Northeastern's undergraduate students for one year is 137% of its endowment, while for Harvard, it's cost of attendance for all of its undergraduate students for one year is, rounding up, 2% of its endowment [1].
It's completely unfeasible for NU to give out free tuition, they'd be in the whole for 100s of millions of dollars. Harvard, on the other hand, could take 2% of its endowment to pay for its students and still have 9% [2] of growth (that's nearly 2.5 billion dollars) to spend. Even if we assume the dismal 5 year average return (which includes 2008-2009's economic shitfest) Harvard would still have 3% or about 700 million dollars of growth to spend (which is to say, their growth is equivalent to Northeastern's endowment).
I could not find any figure on the amount of money which disappears into Harvard Medical school, but if you could dig up those statistics, then we'd be able to see what sort of growth Harvard's endowment would need to maintain.
That said, Northeastern's endowment is hopelessly small, while, with Harvard's endowment, it seems feasible to pay for undergrads, unless Harvard Med's net losses are more than 2.5 billion dollars (or, more reasonably 1 billion dollars).
[1] http://www.wolframalpha.com/input/?i=(harvard+tuition+*+harv...
[2] http://cdn.wds.harvard.edu/hmc/2010_endowment_report_10_15_2...
edit: add "137% of endowment" to 2nd P, remove obviously "It's obviously completely" from 3rd P, note that NU's endowment is about equal to Harvard's growth over a really bad five years, and formatting
Saying that some 1% of kids can get an affordable education at top schools is really quite irrelevant.
If you fall in the dreaded "middle-ground" for financial aid, your options for an affordable education are somewhat more limited, but nonetheless existent.
A rough estimate for the United States could be that ~30 states have good to excellent public universities.
The group that seems to be in the toughest spot are the students from states without excellent public universities and in a bad financial position for aid or grant money.
If you can't get into any of the private schools that will satisfy all of your need, and you're not willing to make up the difference on debt, there are many excellent public schools, (Berkeley, UCLA, UMCP, Urbana Champaign, the list goes on), none of which have very high tuition.