I think it's worth distinguishing between "Computer Science" and "Programming".
One of the motivating examples in the OP is "conversational programmers". OP defines that as people who want to be able to have conversations about programming stuff, but won't program. -- For those people, sure, assuming heavy technical/math background when teaching programming isn't helpful.
But many topics in Computer Science heavily rely on applying math. (3D rendering, Computer Vision, Machine Learning).