It works because well, its actually pretty primitive at its core. Whole learning process is actually pretty brutal. Doing millions of interations w/ random (and semi-random) adjustments.

I think I've fallen into the "it's just a very fancy kind of lossy compression" camp.

Honestly once you understand maximum-likelihood estimation, empirical risk minimization, automatic differentiation, and stochastic gradient descent, it's not that much of a surprise it works.