I'd say its the exception that you should not go Ivy/elite if you get in. Ivy Leagues have experiences/opportunities that simply are not replicated at state schools.
Yes for determined/driven individuals, it may not matter all that much. And if you are not going to take advantage of what those elites have to offer, maybe you should reconsider if the financial burden is too high.
Faculty jobs are incredibly competitive, which means that at almost any school you will get some very high-quality faculty (at least in terms of research, publications, and fundraising.) Non-elite research universities may also offer good opportunities for research. And of course elite public universities offer nearly all of the benefits of their private cousins, usually at lower cost.
But I concur that if you get into MIT (or comparable) and it seems to be a good fit, then it is hard to beat for a variety of reasons.
Nonetheless another strategy that is worth considering is pursuing a science or engineering major at a good but cheaper and less elite school, where you can perhaps stand out more, and then attending an elite graduate school (private or public) in your field.
I don't think that's really true, and if it is I don't think it's an advantage you'd actually want to use later in life. Based of my experience of hiring over the past 25 years (as someone hiring people, not as a candidate), my belief now is that your university degree is important for about a decade, has diminishing returns over the next few years, and then it's basically irrelevant. If you've got 15 years of relevant experience what degree you have and where it's from makes no difference to a good company.
The exception is somewhat antagonistic too - if you still believe it's important (e.g you come to an interview and talk about how great Cambridge is) that's a signal you're not going to be a good hire.
Obviously there are many caveats to this - I don't have an elite university degree, I'm not in the US, I've only ever hired developers, I've never worked in a business that needed people with elite university degrees, the number of people I've hired is a tiny sample of the industry, etc.
I suspect people who think elite degrees are important are mostly other people who have an elite degree, and often those people are the ones who make it into hiring manager positions or higher. In that case it kind of does matter, but only if you want to work in a company where an elite university degree counts for more than experience, and I'm pretty sure you don't.
VCs still care. VC pitch decks will make a point of highlighting the elite schools that early engineers/founders went to (MIT, Stanford, Ivys, Oxbridge, etc). Whether it should or not, having a couple of those big names on there can be the difference on millions of dollars of funding. It might not be important at many levels of the industry, but it's useful to have if you're a founder or early employee in startups.
Yes for determined/driven individuals, it may not matter all that much. And if you are not going to take advantage of what those elites have to offer, maybe you should reconsider if the financial burden is too high.