I think it depends on where you are in the country you live and what your expectations are career-wise. If your aspiration is to work on Wall St. or Madison Ave, it's makes a huge difference where you went to school. If you're looking to work in a small town, local business type career, it matters less.
I agree fully that college aged kids are very impressionable, but I think you have unfairly generalized Ivy League schools and their students/graduates. You are going to find kids who come from all types of backgrounds at any school and I think it's really important to lean how to mix and interact academically, socially and professionally with all types of individuals. Again, depending on your chosen field, you may have no choice but to compete with people from wealthy backgrounds, so why shelter yourself from it? DH and I have not been out of college all that long, and let me tell you, it's a competitve environment in the workforce and to believe otherwise is naive. Again, I don't understand why you think Ivy's are havens for kids who come from backgrounds of entitlement and privilege. What a gross generalization. You are correct though, the Ivy's are doing something right as they graduate many of the best and brightest students every year.