What you will eventually learn is your experience in college is going to be far less dependent on the exact college you attend, and far more dependent on YOU, than this statement implies.
Attending CMC, which of course is a Claremont College as well, will present far more opportunities for special experiences than any one person can possibly do more than a fraction of. Your exploration of those opportunities, your decisions about which to pursue in depth, and what you then do with those opportunities, will end up defining your college experience.
Similarly, what happens next after college, and on from there, is dependent on YOU, again what you choose to do in college, how well you do it, the networks you develop, and so on. CMC and the Claremont Colleges also have all the opportunities and much more than you could possibly need to support such next steps.
And then very, very quickly, where you went to college is largely just a personal memory. What you will again learn is that advancement through life is a long series of “what have you done for me lately?” questions. College admissions specifically is about what you did as of about 17 years old, and no one is really going to care about that when you are, say, 35 and looking for a promotion, or possibly a change of employers, or so on.
However, I understand you may need to actually experience this before you will believe it. But for what it is worth, I went to one of the colleges on your list, and I know all my college friends agree with me about this. It certainly can be a good experience and good education to go to such a college. It just is not as unique as you are currently imagining, and what actually happens from here is truly going to be about you and not the exact college you attend.