I wonder if a problem with math is that there are (at least) two sides to it: Practical and artistic. And I wonder if the practical or useful side of math could be taught today via computation.

Even the useful side of math -- the stuff supposedly taught in service to the science and engineering courses -- is taught with a computer nowhere in sight. Yet people who use math in those fields, including myself, always do it with the assistance of a computer, whether it's to help avoid dumb mistakes or to automate tasks involving large amounts of numbers. And the physics problems that can really be solved with purely symbolic math are few and far between, and rather contrived. It actually leads students to believe that the formulas are false when applied in the real world.

I don't think teaching computation would harm the handful of students who develop an interest in math as a liberal art. If they want to explore, they will, either on their own or with guidance. There's no reason why they can't be introduced to abstract math, and proofs, along the way.