I've written here quite a bit about my school experience and why it doesn't have to put new grads into unbelievable debt. I did freshmen through MS for under $30k out of pocket -- in the U.S and not all that long ago. Looking at the subject the last few years I've no reason to think it can't still be done for maybe no more than $45-50k. Paying off all of my student debt 3 years out of undergrad, then earning enough to cover my M.S. out of pocket is a pretty awesome feeling. (BTW My school's entire endowment wouldn't even add up to MIT's yearly earned interest on their's)
If you really think that your school is where you have to go, most outrageously expensive private schools have a handsome tuition assistance program if you can figure out how to work the system -- these days you can probably get an undergrad from one of those schools for less than I paid for my education. They probably do everything they can not to advertise is. But you have to have lots of chutzpah and don't take no for an answer. Hit the tuition assistance office daily, be a squeaky wheel, adjust your living conditions to suite the requirements for maximum assistance. Need to make less than $x per year? Do that. Need to not be a dependent of your parents? Do that (make sure they take you off of their taxes, you might need a copy). Get extra assistance as a school employee? Get a crap job cleaning floors.
Do not pay the inflated sticker price just to have fashionable brand recognition for a brand that won't matter in the job market in 7 years.
Do the math and optimize. If you aren't willing to do that, it might be worth reevaluating why you went to an "exceptionally expensive" school in the first place.
In my case, with multimillionaire parents who back in the '80s drove one vehicle with a depreciated value of 2 plus or minus years of full costs, no amount of cleverness would have helped with the financial aid office. Due to MIT's horrible money management and youth it just didn't have the money.
As for why I choose MIT, my parents attempted to set up a trap, they were sure I couldn't get into it or CalTech (I'm not a math genius, but good enough to do MIT's required level), so they said it "wasn't worth their money" to send me to any place good but those two. As it turned out, MIT was looking for people like me (ask for details if desired; one less obvious one is that they look for evidence the student can do projects, and submitted a couple of those) and I got in, not that they had any intention of paying more than they could get away with (a saving face sort of thing).
The later experiences of my younger siblings showed that it wouldn't have mattered where I went, except that I probably could have worked my way through the very cheapest possible place, but that was so down market getting into a good grad school would have been iffy. In my field of chemistry, the only none required by the subject accrediting organization courses they offered were analytical lab ones clearly intended for student for whom the undergraduate degree was terminal, for a lab tech career.
Prior to a fairly recent overhaul, the technology licencing office (rough quote from memory from Tech Talk, the Institute's official newsletter): "focused on the details of licencing vs. doing a lot of licences" and averaged a little over 1 per year (!!!). Given that I know 3 of those, the LMI Lisp Machine licenses and the same plus Macsyma to Symbolics....
They notoriously screwed up the 3D core memory patent ($40 million lump sum to IBM vs. the offered 1 cent per core) and a synthetic penicillin patent. Either could have paid for a complete replacement of the entire campus. I very strongly suspect these weren't the only screwups, and e.g. Symbolics scammed an exclusive license to Macsyma mostly to keep it out of other people's hands, one reason Wolfram was able to beat it sort of starting from scratch.
Back then, when the prime rate was over 20%, and inflation was over 15%, MIT was getting a much lower return on its endowment. I want to say 4%, but I'm not sure. MIT does a lot better now, but that is also recent.
It got its charter just as the Civil War started, and set up operations just after. So as noted it doesn't have the 2 centuries or more of additional compounding alumni donations the famous Ivies have.
Not sure when it started, and it was again fixed only fairly recently, but the alumni magazine, Technology Review, was dedicated to telling most of the alumni that what they were doing was evil. And again by then the Institute apparently had convinced a lot of alumni that it couldn't be trusted with unrestricted gifts. In its favor it never tried a Princeton Woodrow Wilson Center type donation theft, then again I don't know of any other top school so brazen.
Ah, it also was wretched, not interested or perhaps in part stymied by city government (which hates Harvard with a passion, and MIT gets some of the blowback) in making money off of local real estate. When I showed up the Kendal Square area had that bombed out sort of look, in part due to NASA deciding after JFK's assassination and LBJ becoming President that, oh, on second though Texas is where we should build our space center. There was almost no housing, let alone vaguely affordable and safe, to be found close to campus. I'm sure that bit of MIT's studied indifference to student welfare didn't escape some of the alumni who were the sort to later make a fortune.
Bottom line: not a lot of money to grant to students, and a total focus on needs based aid. And, hmmm, rather obviously students like me who were crushed by the intersection of the financial aid policies of MIT and their parents would never be in a position to donate a lot of money, and not inclined to donate much of what we do have.