More than Caltech, but the number of US universities that specifically want to see calculus in high school is small: What US universities explicitly state that calculus is required or expected for frosh applicants? - #20 by ucbalumnus (older post, check university web sites for current information)
This is likely because not all US high schools offer calculus (although the number has been growing over the decades), and access to calculus in US high schools is often dependent on math placement decisions made while the student is in middle school. Both may be “tainted” by non-academic criteria (e.g. SES, race, ethnicity, rural), so colleges are hesitant to shut out more potential applicants whom they see as demographically underrepresented. In addition, the US does not seem to favor early specialization the way some other countries do (e.g. in Germany where students go to different high schools depending on whether they are university-bound or trades-bound, as determined in middle school), so there is a desire to keep the doorway to university open as long as possible (while in countries where there is earlier specialization, high school education for the university-bound can be accelerated based on the assumption of the students being stronger in university-prep subjects).