Is that what the data shows, though? I've read summaries of papers describing the exact opposite and linked them here before.
Here's one such example, with a followup comment describing a study that contradicts the argument you lead with. (I'm merely saying it contradicts it; I'm not vouching that the contradiction is correct.)
https://news.ycombinator.com/item?id=30748063 , summarized as:
> For most students, the salary boost from going to a super-selective school is “generally indistinguishable from zero” after adjusting for student characteristics, such as test scores. In other words, if Mike and Drew have the same SAT scores and apply to the same colleges, but Mike gets into Harvard and Drew doesn’t, they can still expect to earn the same income throughout their careers. Despite Harvard’s international fame and energetic alumni outreach, somebody like Mike would not experience an observable “Harvard effect.” Dale and Krueger even found that the average SAT scores of all the schools a student applies to is a more powerful predictor of success than the school that student actually attends.
The link to the article and the followup is in the only 2-deep chain linked above.