The primary value of a Yale and Harvard degree is the networking opportunities (also why the Marines are a good choice for working class kids, Marines tend to hire their own), obviously it helps to have George Bush, Al Gore or Zuckerberg as your college roommate or fraternity brother over Joe Schmo from Penn State. Since most of the students are from upper class or rich families, they have build in networks that are expanded by attending these schools.
The second benefit of an elite college is the peer pressure, I've taught at a couple colleges and the expectations aren't in the same league, students in an Ivy league school don't think twice about a 15 book reading list, my students balked at a 5 book reading list.
The teaching can be worse at a big research university b/c the top professors tend to teach graduate courses and have a light teaching load, but you can get exposed to top scholars in your advanced undergraduate courses.
A PhD is a mistake these days, since the 1980s, tenure track positions have been extremely difficult to obtain, and now are almost impossible, and outside of college teaching, a PhD has limited value. In business and consulting, doing original research isn't valued - what they want is "product", that is, fast turnaround, facile analysis - and because of age discrimination (which starts in your 30s), wasting too much time in academia can deep six your career (b/c if you come out at 30, there's some kid with similar work skills 5 years younger just behind you). MBA and law schools are better preparation for the shallow, quick turnaround work that is in demand, even in think tanks, most of the staff are MBA, MS and JDs, not PhDs.
How is it in the USA with Uni name recognition? Ofc I know it exists as I considered heading to the US when I was 18. But not sure to what extent.
It is not *that* big a deal in mainland Europe (though differs by country, and ofc a few very desirable in different places), but in the UK there are basically "tiers" of Uni... and a crap degree from a good one might open more doors than a decent degree from a lower end uni.
Like from a cynical perspective, roughly:
Tier 1: Cambridge, Oxford, LSE, Imperial, UCL
Tier 2: Manchester, Warwick, Edinburgh, Kings
Tier 3: Durham, Glasgow, Bristol, Birmingham, Southampton, Sheffield, Leeds, Nottingham, Liverpool, York, St. Andrews, Lancaster, Cardiff, Newcastle
Tier 4: Queen's Belfast, Leicester, Loughborough, Reading, Exeter, Bath, Queen Mary, Aberdeen
Would be - for example - the Universities that I would recommend to my children if I had children and raised them in the UK. And, tbh, I would guide them towards tier 1, 2 or 3 unless specific courses at a tier 4 or they really loved the place.
Ofc... then have some specific schools that are very highly regarded. Say Brunel University and Mech Eng degree there. Amongst others that for specific courses would be a good idea.
But - really - those ~30 (especially the 22 in the top 3) are the ones that you get the most "value" in terms of name recognition going forward.
It is snobby and awful. As you said there is better teaching at some of the Unis not as "highly regarded"... but that is the world we live in.