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.
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.
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.
(Which it probably won’t)