I agree BC is not light, not at all. I question, though, if a kid would be fully prepared with just BC, and even if prepared, will they get in to CalTech. It seems to me that BC is the bare minimum for these schools. Maybe I’m wrong, but I’d surprised if either accepted many AB student last cycle. Heck, AB seems to be the bare minimum for liberal arts at the Ivies.
Also, OP has said their school offers a number of post AP courses. If ten or so kids take MV or DiffEQ as seniors, OP may not be seen as having taken the most rigorous courses. This was my primary point. Sure, if your school doesn’t offer calculus, you have to be creative and have the money to take it via BYU, UC Scout, dual enrollment, or the like. But, if you don’t take at least AB, are you really going to apply to MIT or CalTech and will you be accepted?
Even where I live—and I don’t live in Arlington or Palo Alto—it is becoming commonplace to see kids get to DIffEQ by senior year.