I'm very curious about which university this is, because as far as I can tell the stats for getting into Harvard are significantly higher than getting into any UK school.
Most Oxford courses, for instance, require a 1400 on the SAT, combined with three 5s on AP exams. Harvard doesn't have requirements, of course, because US schools don't have requirements; it's much more flexible than that. However, the average SAT is a 1510, and the 75th percentile is at a 1580 (which is near-perfect). Most Harvard entrants who have a full range of EPs at their schools (which isn't true for all schools; Harvard draws from poorer and less provisioned schools as well) would be startled at the low bar of just three 5s--they would expect most students to have at least five or six.
It's true that American schools stay far more general for far longer than UK schools; you'd have to go through at least an MA degree in America to get to where UK students are at the end of their BA. However, along the way you have significantly more exposure to other subjects, which, at its best, promotes lateral thinking, creativity, and curiosity. A lot of British students will, for instance, stop taking a language, or a science, or a literature at the age of 16. In America, you more or less have to do all of those things until at least your sophomore year of college, or around 20. British courses are far deeper and more specialized than American ones, on the other hand.
It really depends what you want an undergraduate education to do for students, in the ideal: make them skilled specialists or make them broad, creative thinkers. One isn't better than they other; they're just different.
In terms of admissions, at the big state schools, it tends to be your stats alone: your GPA (based on coursework throughout your four years of high school) and your standardized tests, either the ACT or the SAT. Some don't even require essays or recommendations.
At your most elite universities, which have huge admissions teams, it's also very much based on letters of recommendation, extracurricular activities, personal statements that talk about your perspective on the world, supplemental essays, contextual information, (sometimes) interviews, relationship to the university, particular skills or perspectives you might bring to campus/the classroom, the rigor of your coursework, and then your GPA and your SATs.
Finally, yes there's an increasing expectation amongst the professional classes that you'll do some form of education beyond your BA. These include academic degrees (MA, PhD), as in the UK. But they also include law (JD), medicine (MD), business (MBA), policy (MPA), etc., as well as vocational MAs (e.g. MA in advertising). There are no law or medicine undergrad degrees, and most big corporations will want you to do an MBA at some point, though they'll often pay for it.