I’m not sure you understood my point.
I think Princeton and Harvard and many other US colleges are skeptical that they cannot help their students improve their intellectual skills between the time they enter and the time they leave.
Indeed, but they may also expect you are going to be more prepared for certain challenges as a junior or senior than you were as an incoming first year.
As an aside, there is a lot going on behind that observation. [Edit: consider this an elaboration on prior posts with similar content.]
One factor is simply numbers. The US has a much bigger higher education system than the UK. And if you do some math, Oxbridge make up a larger percentage of the relevant UK undergraduate population than all the Ivies combined do of the US system. In fact you need approximately 20 or so private colleges (the Ivies, some of what we call Ivy+, and a maybe a few of the most selective Liberal Arts Colleges) to approximate the Oxbridge percentage.
Another factor is that these colleges practice what is usually called holistic review, in which academics is only one component along with (generally speaking) activities (not least of the sort that are valued student activities at these colleges), and various personal/fit factors. Holistic review is actually tied to the Liberal Arts and Sciences tradition, because the idea is that your education does not just happen in classrooms, libraries, and laboratories. It also happens in your dorm rooms, and dining halls, and during activities, and in the bus rides to activities, and so on. And they want students who will both value those interactions, and contribute meaningfully to them.
One of the consequences of holistic review is to increase uncertainty, because many of these factors are hard or indeed impossible to reliably measure. Indeed, these colleges are not actually trying to get all of one sort of student, they want to mix together different types of students, and whether or not they admit you in particular may depend on what other similar sorts of people apply in that given cycle.
And that uncertainty invites more applications, as many people cannot rule themselves in, but also cannot rule themselves out. And then some people who probably really should rule themselves out apply too.
So they end up with very low acceptance rates. And if you could filter out the unrealistic applications, they would be a bit higher, but still pretty low. And those people with realistic applications simply do not know if that college, that year, will decide they want that applicant in their mix.