Prestige is the eye of the beholder, and what is considered “prestigious” in one region is not always as prestigious in another region, and there are regional preferences as well.
In many states in the SE and Midwest, the state flagship often has more prestige than any Ivy league. So Ohio State rules in Ohio, U Alabama in Alabama, etc. Moreover, there is also often a general suspicion of East Coast Schools in many places outside of the NE and Mid Atlantic.
Moreover, as @HighTide2020 correctly states, the biggest advantage of attending a “prestigious” college is the networking, and most people grow up, go to school, and settle down in the same general region. So there will not be many people in Omaha, NE who attended Yale, but there will be a great many who attended U Nebraska, Lincoln.
In the business and law world of the NE and the Mid Atlantic, I would assume that the Ivies, MIT, and the “elite” LACs reign supreme. However, the further you get from there, the less people are impressed by degrees from these schools. I am not sure how many people in Idaho have actually heard of Brown, Dartmouth, or Columbia, while it is likely that even fewer have heard of Williams or Amherst (I’m not even mentioning Bowdoin, Middlebury, Colby, etc).
For the vast majority of the positions for which people apply the difference is between whether a person has a degree or not, rather than where the degree was awarded