Maybe that doesn't matter in CS/programming, but it does in lots of other (e.g. Engineering/Science) disciplines.
Based on everything I've seen over my roughly 20-year career in academia, plus the 18 years before that living in that world (my parents are both professors), what you get from going to Stanford, MIT, Harvard, Yale, and all the other "Big Name" schools is just that: the name.
The education you get there is not better than the education you can get at a small liberal arts college—in fact, it's often worse, because you're just one of tens of thousands, lost in the crowd, and you're extremely unlikely to get one-on-one attention from the professor if you have any trouble with the material.
Small liberal-arts colleges, on the other hand, so long as you're avoiding the ones that are specifically party schools, generally tend to focus much more on the teaching aspect, and especially on the personal attention aspect.
For more specialized degrees like engineering you may need to narrow your pool of those schools to find one that has a good program, but there are enough that unless your field (at undergrad level) is suuuuper-niche, you're very likely to be able to find one that works for you.
And while it's not universally true, they tend to be pretty good about taking transfer students.
I want to be very clear that I'm not saying "you shouldn't go to these schools"—I'm saying "if you go to these schools, recognize that what you're getting that you won't get anywhere else is not a better education, it's the school's name."
So I find your comments quite curious. Nowadays I tell my younger cousins and nephews/neices to research the faculties in colleges they are applying to and look at the quality and impact of their publications.
Sorry if this sounds harsh, also I'm not trying to deliberately shit on my uni education, but let's just say I didn't find it great for many reasons. One course by a "leading expert" could have been pretty great, just that it was done in not so stellar English (the prof was German, so am I) and so it wasn't so great to understand.
If you just show up to learn and don't plan to stay in academia there (do a PhD, get to know the faculty) I really don't see a point.
A university having a prestigious name is not synonymous with having Nobel Prize winners and influential professors. Hell, one of the professors at the small liberal arts college I work at is a Pulitzer Prize winning poet.
The big thing you get besides ‘the name’ is your relations and links to your cohort. That really helps get good jobs!
I was an arrogant superstar before I went to MIT. It wasn't that I thought that I was worth more than other students, but I felt my classes were a bit below me. I got all As, except for a B or B+ in my Intro to World Politics class at the UofM. As I remember, the way honors GPAs were calculated, I my GPA was above 4.0 at the UofM. In my high school "Enriched Chemistry" class (one level above honors, no extra GPA boost beyond, but all the kids there really wanted to learn), after I caught a couple of mistakes in exams, the teacher started marking my Scan-Tron answer sheets as the exam answer key, and in class, the whole class would together grade my exams the day after the exam to make sure the answer key was correct. There was one exam where the second-highest score was 90/100, so the teacher just added 10 points to everyone's score. At some point, I made one mistake the whole semester, so I ended the semester 9 points above 100%. At the UofM in my honors mathematics course, I was being graded on attendance and felt it was a bit of a waste of my time. I would read a newspaper in class. One day, the TA asked a couple times if anyone knew the answer to a problem, and I made a bit of a show of folding up my newspaper and proceeding to answer the question nobody else could answer. The honors math professor took me out into the hallway and proceeded to tell me "I don't care who you are. I don't care what kind of grades you get. If you bring a newspaper to class one more time, I'll have you thrown out of the program."
MIT was another level of challenges and expectations. Most of the kids there were used to being at the top of their class and getting cut a bit of slack from the teachers/administration because they were head-and-shoulders above their peers in high school. For most of us, it was a big ego hit and a big adjustment having to work very hard just to get a median grade.
The instruction at MIT was top-notch, but the real value was increased expectations, and excellent peers for both competition and support.
On the flip side, the ego hit is soul-crushing for some students.
The honors programs of state schools definitely have students every bit as smart and capable as people at MIT. The extra level of competition and expectations at MIT really does help some people shine, though. Also, the name is helpful as there's a pretty high minimum bar for getting an MIT degree. You might not be getting the best by hiring the MIT grad, but you're hiring someone who's pretty good.
That being said, I hope the age of GitHub, HackerRank, etc. diminishes the effects of brand-name schooling. I had a friend back in my honors math classes who also got into MIT, but couldn't justify the expense due to his dad being a welder and his mom a homemaker. MIT offered him a lot of loans and grants, but he got a full scholarship at the UofM honors program and could live at home while going to school.
That said, brand matters.
MIT now invests incredibly heavily in brand development, compromising integrity, research quality, and teaching-and-learning. For grads, that's paid off. My degree has gone up in value a lot over the years.
Absolutely false for STEM fields. Except for Stanford/MIT your flagship public school is probably a better tech school than any other private name-brand school. Yale is an ordinary tech school, with several public schools (Berkeley, UCLA, UCSB, UWash, UIUC, UMich, Ohio State, Penn State, Wisc-Mad off the top of my head) being significantly better and cheaper. And all will allow you in from community colleges.