International95, I went to U of C and had Mearsheimer for a class a long time ago. I don’t remember him that well, but he wasn’t famous then. 
I am very proud of my U of C education.
With that said, I think you don’t realize how prestigious Amherst and Pomona are. Not all LACs are the same, and Amherst and Pomona offers its grads just as strong an opportunity as the U of C for getting into top PhD and professional programs. Moreover, Amherst in particular has a much stronger alumni network for getting job connections after one graduates. Amherst may be small, but it has understood the importance of alumni networking for the past 200 years, whereas the College at the U of C is just getting on board now with connecting together its alums.
(disclosure - I went to the U of C but my daughter has just chosen Amherst)