So this means that only less talented people will end up with huge student debts? I mean, what percentage of the students will qualify for a scholarship?

It really depends on the university. There are two types of scholarships, need based and merit based. As you can probably figure out, merit based works off your grades and scores, need based depends on your family's income. The more prestigious and richer a school is, the more need-based aid they can afford to give. The most prestigious schools are so rich, they can afford to "meet everyone's need" which means they don't even have to offer merit based aid. For example, Harvard is completely free, including housing, food, and books, if your family makes under the US median income. The vast majority of Harvard students get scholarships; there are kids with family incomes of even $150K and up at Harvard who are getting scholarships.

Now, what if you don't have the grades/scores get into one of those really prestigious schools, but the private schools you did get into didn't offer you enough scholarship money and you can't afford them? In that case, you're best off going to an in-state public university where you can pay the lower tuition.