I object to your glibness. Probably both methods (first-principles cognitive modeling vs. high-degree-of-freedom black box learning) will prove informative, just in different ways.
Or in your terms, we may not get to pick the prettiest models, but we owe it to ourselves to explore the space of models to see if we can find the structure in it.
The engineer in me is pleased by the undoubted success the data-driven learning culture has had on problems of real importance. But this work is highly empirical, with a tendency to point solutions, and someone is likely to come in later on and generalize these methods (e.g., why do some families of black-box predictor or features outperform others for language learning). There's room for both approaches.
Norvig's reply to Chomsky's original remark contains a reference to Leo Breiman's well-informed remarks on this question (http://projecteuclid.org/DPubS?service=UI&version=1.0...).
Breiman, as author of basic books on measure theory as well as on classification trees, was able to walk both sides of this line ("make a first-principles model" vs. "use lots of data"). He spent considerable energy over the years trying to introduce the data-intensive approach to conventional statistics. For instance, he was one of the handful of bona fide statisticians who would attend and contribute to neural net and machine learning conferences. Probably this strategy is more productive than Chomsky's grumpy-old-man warnings (or sagacious warnings, depending on how you look at it).