I also did pure maths (mostly differential geometry and things related to that). As well as I guess an equivalent of a "minor" in applied maths (numerical analysis / computer vision / crypto)
My view is that I never expected the maths program to teach me any of those "real life" skills since my university had separate applied maths and statistics programs, each in their own departments. I think in any university degree program you learn how to learn things, and that is useful when learning about new methods or tools or models.
IMHO, the pure/applied distinction is part of the reason why academia is falling apart. The history of probability theory shows that we can have both (i.e. an elegant axiomatic theory of gambling).
