You are so wrong about Northwestern’s STEM.
Northwestern has top programs in chemistry (7th), material sciences (2nd), industrial engineering (4th), and BME (9th). Its math and most other engineering are in the top-20. Furthermore, its integrated science program (ISP) is as good as any science program in the country, including those at MIT/Caltech, as evident by the fact that 3 ISP majors won Goldwater in the same year several years ago, whereas most peer schools had no more than 2 winners.