I agree that lower division math courses should focus a bit more on theoretical material and less on computation, to a degree. This will help serve both the engineers, physicists and mathematicians. However in an engineering class, which is where I learn alot of the math I use, there simply isnt enough time to go over the proofs and ideas behind a mathematical construct. I too learn math better when I understand the meaning behind it. For example I've learned Laplace Transforms in a math environment and Fourier Transforms in an EE environment. I am much more comfortable and knowledgeable about laplace, simple because I've seen the various proofs and theory behind everything I use. I like my Signals book because when explaining various mathematical Ideas they'll usually provide a short informal proof and historical footnotes, enough for me to get a bigger grasp on the material without getting bogged down with the formality of math.
So I completely agree with you, which is why I've also decided to double major in Mathematics along with EE.