The data contradict your assumptions (where are you getting these perceptions from? genuinely curious).
According to internal data from CMC and Pomona, Harvey Mudd is the #1 destination for where courses are taken. For instance, at CMC, 300 students took a course in Fall 2015 at Mudd (followed by 221 to Pomona, 133 to Scripps, and 88 to Pitzer). I don’t have specifics for Scripps and Pitzer, but I’d expect a similar pattern due to the explosive popularity of CS and full access to Mudd’s distinguished CS program as an off-campus major. Some physics students across the colleges do take advantage of the engineering courses. I know one student from my class year who took at least 7 or 8 of them, conducted engineering research with a Mudd professor alongside physics research with a Pomona professor, and went onto a mechanical engineering PhD at MIT. At any given semester, my experience is that ~5 Pomona students take E4 at Mudd (Introduction to Engineering Design and Manufacturing). Some environmental analysis majors do the Environmental Physics and Engineering track at Pomona with some courses at Mudd. There’s a popular 3-2 engineering with CMC and Mudd for management engineering (BA econ + BS engineering), and Scripps has that option as well, so that drives additional 5C movement.
Out of the total number of registrations at the 5Cs, 47.6% were cross-registrations at another school. The extent to which the schools collaborate is significant. There are some limits, but they don’t apply to the many intercollegiate departments across the colleges.
Not many LACs offer a public policy major, from what I can tell (distinct from politics or government). I can only find it at Pomona, Hamilton, Lafayette, and Trinity College. It’s a unique major that requires a substantial internship component. Urban studies, same thing, though a few more have it than PP. In the research I just did, half of the top LACs seem to have education courses, while the other half don’t, so I’ll correct my stance regarding “most LACs”. The point isn’t about specific majors though (there are many others I didn’t reference)- just the reality of the collaboration and the access to off-campus majors which give CC students a wide breadth of options.
What is your point about athletics? Hypotheticals don’t change the reality. It is not apples to oranges- they compete in NCAA Division III. Furthermore, the NESCACs have more athletes and more varsity teams. According to government data, there are 417 varsity athletes at Pomona-Pitzer and 512 at Claremont-Mudd-Scripps. Williams has 744, Wesleyan has 604, and Bowdoin has 635. Also, the combined schools aren’t that large- PP is 2700 while CMS is 3200- around the same ball park as Wesleyan.
Keck is a school I’m not too familiar with. It’s extremely tiny, with under 500 students. It’s not in the central part of the Claremont Colleges but rather a mile away. Theoretically, any biology/related fields declared major could take a course at Keck, not just seniors, but I’ve only heard of one student taking a public health course there. Their website says you fill out a form if you’re interested in their courses. CGU is much more popular, especially for math (https://www.cgu.edu/wp-content/uploads/2017/01/CGU-IMS-GraduateMathCourses.pdf), education, and economics/management. Education courses are open to all, math and econ courses are restricted to majors. Research is primarily 5C based since students take far more undergrad courses than grad ones, but as mentioned, some 7C research labs like the Game Center are at CGU. One can visit the CGU and Keck website and look up research for their various schools- faculty, their research interests, and contact info is described.