I agree the traditional math high school/college math curriculum isn't very worthwhile any more, if it ever was. Just as one example, you'll never use Euclidean geometry again (except the most basic parts that only take a couple of weeks of the standard course), whether or not you continue to more advanced math. Even engineers rarely if ever use the many dry and specialized "advanced integration techniques" that are taught to everyone in calculus.
However, I would revamp high school/college math rather than discard it. There is plenty of valuable and relevant math (e.g., statistics, logic with application to critiquing claims made in the media) that could be taught today instead of a lot of the more abstruse parts of algebra/geometry.
FWIW, when I taught calculus to english majors in grad school, I chose one day a week to teach other areas on general interest in mathematics, which seemed to work pretty well. My students performed equally on the calculus final to the other sections, but many more of them signed up to take additional math courses than in the other sections.