Absolutely. But the simple fact is that high falutin’ mega prestige professor is not likely to be found at Podunk Directional State U, if for no other reason, top privates have more dept money to spread around. High falutin’ prof might not care about the extra money personally, but their grad students will certainly benefit from the extra riches. Compare for example, Stanford grad students who receive lotsa funding vs. Cal’s grad students who are on strike for more $ and benefits which Stanford already offers.