"While calculus has applications, I'm sure other branches of math have applications just as well."
Educating yourself on the applications might answer your question. And make your teaching more informed.
I have been a chemist, engineer, military officer, and finance professional and dabbled in applied psychology and economics. Calculus is needed for that stuff. Number theory is not.
Math courses are arranged (in high school and first couple years of college) to service the mass of students who ARE NOT math majors. Learning about their courses and what math is involved in their HW problems, derivations, etc. would help to inform you on why certain classes are part of a standard curriculum and others are not.
P.s. Richard Feynman (pretty good math guy, won the Putnam with no study as last minute team member at MIT) started out as a math major. He ditched it because 'the only use of the things you learn are to become a math professor and teach more math majors'. He went to EE instead and then to physics.