I'd be curious about how success is defined here. Career is a pretty narrow lens to define it by so I'd hope for something more expansive.
Many of the benefits of having friends in high places are outside of traditional career ladder. The expedited (insert annoying process here), the vacation you're invited on, the unintentional influence you have on some big thing because you happen to be an ear to the decider, etc etc.
Edit: [2] expands the measures to include educational attainment and family outcomes. Reference [3] relates to socio-economic class, while [1] relates to race/ethnicity. [2] was the one I had in mind during my original comment.
[1] Krueger, A., 2012. Estimating the Effects of College Characteristics over the Career Using Administrative Earnings Data Stacy Dale Mathematica Policy Research.
[2] Ge, S., Isaac, E. and Miller, A., 2022. Elite schools and opting in: Effects of college selectivity on career and family outcomes. Journal of Labor Economics, 40(S1), pp.S383-S427.
[3] Dale, S.B. and Krueger, A.B., 2002. Estimating the payoff to attending a more selective college: An application of selection on observables and unobservables. The Quarterly Journal of Economics, 117(4), pp.1491-1527.
It also depends on what the "lesser" schools are. I expect that if someone missed out on the significantly random admissions lottery to get into Harvard but were admitted to Dartmouth, Cornell, or Williams (or even UMass Amherst) instead, I expect that if they'd have done well at Harvard they'll do just fine.
I expect for the lower socio-economic students, the delta is probably related to being among fellow students who maybe set a bit higher bar than other schools would.
That's one explanation, but not the guess that the study author's had:
>"One possible explanation for this pattern of results is that highly selective colleges provide access to networks for minority students and for students from disadvantaged family backgrounds that are otherwise not available to them."[1]
[1] Dale, S.B. and Krueger, A.B., 2014. Estimating the effects of college characteristics over the career using administrative earnings data. Journal of human resources, 49(2), pp.323-358.
The one caveat that did get a benefit were low socio-economic students, who did see a measurable difference in success. That's a class you didn't mention in your post. The thought is that it's precisely due to the network effects.