I strongly believe that it should be taught that mathematics is the basis for all of physical reality. It is the language of the cosmos. Math should be infused into everything, because when it is, there is a better understanding of what you are learning, and this is at a fundamental level.
According to Decartes, every subject revolves around mathematics. Mathematics is the foundation of most subjects, especially the sciences, something science has always acknowledged. Note the calculus requirement to get into med school. Teaching a subject without its foundation leads to lesser understanding and greater struggle with that subject. Mathematics isn't really infused in other subjects; it was already a part of those subjects.
I am the worst mathematics student in the world. I could never see the use of sitting in math class and working with numbers. My brain was more creative. I feel that if the practical use of math had been infused in all subjects I could have comprehended the theories more and would have paid more attention in math class.
Mathematics exist everywhere. To deny this is to deny reality. Ask any baseball fan about statistics and why he cares about them. Ask any politician why he does opinion polls and why he cares about them. Ther really is no subject in life where math is not involved. Even psychology majors rely on test results in human experiments.
No, the infusion of mathematics in other subjects is not unnecessary, because the real world does not allow a person to work with one subject at a time. Mathematics is important in every field, from writing to science to history. It is doing students a disservice to only talk about it in math class.