I could never understand some people's obsession with only learning things of immediate and obvious use. You should study math for much the same reason you study Shakespeare: to learn to think about things you had never thought about before, in ways that you had never imagined to exist.
So when people learn history, for example, they should get some stories that help them define their national identity, in the long term. but if they just learn a bunch of dates that they forget a short time after the test, they just wasted their time.
Does math, as taught today, have long term value? for non technical people, i'm not really sure.
My own maths ability increased dramatically when I got interested in astronomy, likewise trying to write games in basic.
With programming, it's much easier to motivate the subject matter - students want to learn the math so they can improve their projects.
Similarly, I found linear algebra and linear programming much more interesting when I was studying economics, and classical physics much more fun when writing little javascript animations.
So maybe applied math is a better approach at the intro levels. I'm just not sure how we get there from existing math-centric teachers and curricula.