At which top universities can I be the least well-rounded?

Brown and Amherst have the most minimal general education requirements among highly selective schools.

MIT, Caltech, and Harvey Mudd have core curricula that include other sciences besides math and physics (biology and chemistry), as well as voluminous humanities and social studies requirements (including breadth and depth subrequirements):

http://web.mit.edu/hassreq/
http://www.ugcs.caltech.edu/~arc/files/hss_reqs.pdf
https://www.hmc.edu/hsa/wp-content/uploads/sites/25/2014/01/Concept-Map-of-Requirements-111414.pdf