Well, I admit I'm a bit more familiar with the humanities, but in general masters programs work differently - terminal masters candidates, i.e. those not  doing the degree as the first stage of their Ph.D program, do have to pay. Back when I was applying the rule of thumb was that some private programs had a two tier system for those admitted into the doctoral program - some students getting a five year deal - no tuition, stipend, three year teaching requirement - some getting no aid - these have been being phased out. The others, including Stanford, gave full rides to everyone they admitted. The public ones generally had year by year financial aid systems - i.e. you had to reapply each year, with of course a teaching requirement unless you get outside funding.

 The ten billion btw, provides a good chunk of the operating budget which a quick google tells me was $2.6 billion (not including capital spending or hospitals). Just over half of that goes to salaries and benefits. Nineteen percent comes from students.  Sixteen percent comes from the endowment, another five percent from non-endowment gifts. With the long boom market and the somewhat related increase in giving, the endowment has been skyrocketing. But using a bit over 4% of the endowment for current spending, which I believe is pretty typical, doesn't sound that strange as a long term conservative approach. These are very wealthy institutions but they also spend absolute fortunes.

I think you are not living in a parallel universe, but perhaps you are not properly understanding the graduate school enrollment issue. My daughter went to a prestigious east coast school for graduate school (M.A.) and it cost about $2000 a year, mostly for airplane tickets home. She had a small scholarship, a teaching assistantship, and a summer job, and has no debt at this point. Many of her friends are in similar situations.

The American system, like the French system, must be properly "played," but it is perfectly possible to get into a good school, if you have good test scores and grades, even if you come from a poor family and a third rate high school, and, further, if you fall off the tracks for a few years, it's possible--although hard--to recover and make up the difference later.

Further, the cost of excellent state schools is a complicated formula where all costs and benefits are not immediately apparent. For example, the University of Colorado, a huge state school with about 25,000 undergraduates, boasts several Nobel Laureates and has a broad range of leading programs. Cost for out-of-state students is about $32k per year (all inclusive), comparable to the cost of high-end private schools. The in-state cost is around $15k, which I know sounds outrageous to Europeans. However, this does not take into account grants, rebates, and special case situations that apply to many students. For example, there is an automatic state reimbursement of (I forget what, about $1000 a year) that everybody gets, and funding from the state College Opportunity Fund worth about $1400. You can get federal Pell grants for up to $4000 a year, FSEOG grants for up to $2000, CLEAP grants to $2000, and a bunch of others. You can get a full scholarship by signing up for the military via the ROTC program. Also, most churches give small scholarships to a few students, as do small businesses and parents' employers.

In addition, the state school systems have a broad range of opportunities. In Colorado (which is not unique) there is the very highly rated School of Mines, the excellent Colorado State University, a number of smaller four year schools like Western State, for example, plus extension schools located at remote sites (e.g. CSU has a small campus in Pueblo, 200 miles from the main campus). Also there are two year schools that allow kids who didn't quite make the honor roll in High School to take basic classes that are 100% transferrable to the regular colleges, at a fraction of the cost. Pikes Peak Community College in Colorado Springs, for example, costs about $200 per credit hour (16 hours being a typical full course load).

So the bottom line is that there are some kids who come out with huge loans, but plenty of others don't, or have only small loans.

It very much depends on what you are studying.

In some disciplines, yes, there is no excuse for paying for a PhD.  (These include subjects where you won't earn enough money afterward to pay back loans anyway.)  In others, you incur lots of debt.  Sometimes it's a combination.

My sisters and I are good examples.  We went to different grad schools in different subjects.  I paid almost all of my grad school expenses through loans, one sister got funding for about half of hers, and the other was completely funded and paid nothing.  Each situation was normal for our respective fields of study at the time.

And yes, there is dramatically less funding available for foreign students, at least from the universities and programs themselves.

In my grad program, most of our international students were funded by the US government, oddly, which had several programs set up for students from "emerging democracies."  Thus we had students from Eritrea, Albania, Azerbaijan and Hungary, but none from France, the UK or Germany.  (We also had students from India, Tawian and South Korea, but their funding was different.)