In the UK, getting into Oxbridge is nowhere near as difficult as getting into Harvard, Yale, Princeton. There are 24,000 undergraduate spots at Oxbridge for 60 million Brits, compared to 17,000 spots at HYP for 300 million Americans.
Also, the application criteria at Oxbridge is far simpler. It is based entirely on academic potential. British universities are uninterested in extracurricular activities and "well-roundedness". In the US, very smart students with perfect grades are rejected from Harvard because they weren't editor of the school newspaper, because they got a D in History in 9th grade, or because they couldn't write a good essay about "If you were going to sing a song in a talent show, what would you sing and why?" That doesn't happen in the UK. If you are smart, work hard in school and get good grades, you'll get into Oxbridge. The same can't be said for getting into HYP.
All of the British universities are public, so there doesn't exist the situation where students may choose to go to Berkeley instead of UPenn because they want to save money, or because they were offered a scholarship.
Which university you attend in the UK tends to be a better indicator of intelligence and academic success than where you study in the US.
From what your saying, that makes Oxbridge rather attractive for many people on this site, who were never interested in being "well-rounded" just for the sake of university admission.
However, I do think that the emphasis on the prestige of one's university in this country (these days, at least) largely stems from a good decade or so of policies pushing perhaps less-than-ideal candidates into higher education. The replacement of vocational training with degree-level equivalents has in many ways depreciated the whole university process, leaving employers necessarily needing to look for the 'value' of a degree anywhere they can.