As a counter-anecdote, however--when I was at Harvard, I don't think I ever felt separated from professors. I spent a healthy amount of time interacting with professors from many disciplines, in the classroom, through research, and even casually. I found even the most respected professors accessible, and enjoyed discussions with them.
Harvard may be a special case; I'm not to judge other schools without experience. But I will say that I actually miss that climate a bit, rather than having tried to escape it.