I would argue the opposite problem: those who are interested in math at the college level are forced to sit through two years of applications-based mathematics

I would argue the opposite problem: those who are interested in math at the college level are forced to sit through two years of applications-based mathematics before ever touching the theory behind it. Nearly all of higher-level undergrad mathematics is hidden behind courses designed to teach engineers problem solving techniques using calculus. As a result, the intro calc courses don't do a particularly good job of imparting either theory or applications, unless you have an unusually talented professor. I came out of Calc II being able to solve some nasty integrals only to realize that you really only need a couple simple techniques, and with no idea how to set up problems until I went through a few physics courses. What was the point of all that - we could have learned integration by parts and u-substitution in a two week session and moved on, or actually spent a semester of analytical work preparing for higher level math. (edit: differentiation -> integration)