Good point... The realization that chaotic systems are ubiquitous, and that many physical phenomena (motion of the planets, how chemical interactions work at the electron level etc) can't be modeled analytically (so far as we know) was a big upset to mathematics and science, and still isn't addressed well in school curriculum.

To expand on your main point: A loose, but appropriate analogy is that FP appeals to programmers in the way analytic solutions appeal to mathematicians and scientists: Neat, ideal, beautiful... but a poor fit for many practical problems.