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But I'm getting the impression that MIT is full of those who relish rigor not for the sake of learning, but for the sake of showing off (even among other MIT students)
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Who says that it's an either/or situation?
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I'd much rather hear about how the "rigor" helps one learn
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To give a very simple answer...I learned more from being in classes where more is expected of students. I learned to think differently, as well. And I think I am a better person, a better student, and a better worker, because I was challenged, and because I had to work hard. I think I value my degree and my education more. I am certainly more resourceful.
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and how that learning can be applied to help the world.
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I don't think rigor itself necessarily does much for this. I think MIT's emphasis on theory and applications going hand-in-hand, and the combination of intellectualism and enthusiasm for hands-on work among the students, does more for that.