I go to one of these elite schools and the primary benefit is in the connections you make. However, the worthwhile connections are generally only available to those who would have been successful regardless. For example, when I look at my friends who've landed the best jobs/internships they overwhelmingly got their interviews due to who they knew at the company already, which mainly came back to either who their parents knew (largely related to how wealthy their parents were) or what social club they were in (again, largely correlated with wealth).

So yes, the connections at elite schools are great, but they primarily serve to reinforce the same social structure that already exists. That said, there are certainly exceptions and it is possible to make these connections if you come from a less privileged background, but the odds are against you since you 1) don't know where to look to make these connections and 2) aren't like the people who you want to make connections with and so you're less likely to connect in the first place.