I'm worried that in presenting math with visible, tangible intuition dominant will do more to silo the knowledge inside the ivory tower.

N-variable calculus isn't something that you can draw a picture of. Lots of (very practical) Linear Algebra is derived from the pure "Linear Transformation" interpretation rather than the "Matrix" one. Stochastic...anything (seems to be all the rage these days) is not made with helpful pictures.

If we train people to do math in a non-abstract way, they won't be as easily able to grapple with the real problems, which are only approachable in the abstract.