Even very high scorers sometimes find it impossible to get into top schools. Part of the problem is supply of slots has not kept up with population growth. It's not like Harvard's enrollment has kept up with population growth. Another problem is that the ceiling of standardized tests has been lowered, so top scores more more common.
I know a guy who got a perfect on his SAT at my lower middle class suburban high school back in 2004 or so. He got rejected from Harvard. Even the most prestigious school around the Kansas City Metropolitan area only gets 1 or 2 people going to Ivy League schools every year out of maybe 200. Which I think is funny because they definitely bill themselves as an “Ivy League Prep” type of school.
Universities like to limit themselves somewhat because they don’t want to endanger the brand, but it takes an insane amount of money and effort to get a new college or university off the ground.
The state schools may be able to sidestep this a bit.
Not just an insane amount of money and effort, but likely decades to develop a reputation that could rival that of a Harvard or MIT. When you're starting from zero, you're not going to be able to attract top-notch faculty.
