People absolutely do apply to multiple Claremont schools, if there are several that fit what they’re looking for. (I’d expect the appropriate overlap maxes out at 2-3 schools in most cases, though.) Mudd is definitely STEM-focused (although it still bills itself as a STEM-focused LAC), but fewer than half are engineering majors (although if you combine engineering and CS, you’ve accounted for more than 2/3). In any given year, around 7-13% major in physics or math+physics. For your son, probably Pomona and Mudd are the ones to consider; a female student with the same interests might consider Scripps as well. The question with Mudd would be whether their intense core curriculum appeals. https://www.hmc.edu/academics/common-core-curriculum/
At Pomona, physics occasionally cracks the top 5 majors but usually not; the percentage of physics majors is under 5%, but Pomona is twice the size of Mudd so the cohort size is similar, and with cross-registration, the Mudd and Pomona physics majors probably end up overlapping quite a bit in upper-division classes.
Curriculum-wise, Mudd is the least integrated into the consortium because of its heavy core requirements; but Mudd students still register freely throughout the consortium for electives. My daughter, who’s a senior at Scripps, has taken classes at all of the colleges- two at Mudd, and even more at each of the others; she’s dual majoring with her primary major based at Pomona. Not every class is open to cross-registration but the vast majority of non-core classes are. Athletics (varsity, club, and rec) are split between Pomona/Pitzer and Claremont/Mudd/Scripps, so if a particular club sport is of interest, Pomona vs. Mudd would be a different team.
Architecture-wise, yes, each campus has a different aesthetic, but students can enjoy all of them. Being able to graze freely at the 7 dining halls across all 5 campuses is a plus as well, in non-pandemic times. (There is of course an app - developed, not surprisingly, by a Mudd student - that consolidates all of the menus for ease of choosing where to eat.)
Overall, it would be a noticeably different experience to be based at Mudd vs. Pomona, but from what you’ve said about him, I could imagine his preference going either way.