I feel there is excessive emphasis on "what Chomsky said" and "what Chomsky did". Norvig chooses to point out that the principles and parameters framework is, let's say, imperfect, but, well, Chomsky would agree. Moreover, if you zoom out and stop obsessing about quotes from "Syntactic Structures", you will realize that a lot of the work that's being done in theoretical linguistics is not quite as barren. Yes, statistical methods for (say) anaphora resolution can be extremely efficient, but basically very few people had thought about anaphoric relations in any systematic way before generative linguistics came around.

Moreover, rule-based NLP approaches also have their place, and they are often the direct result of theoretical advances. A case in point is the modelling of morphophonology (which is necessary for spell checking, dictionaries and text generation for morphologically complex languages): many successful approaches are those based on finite-state machines, which could not have happened without Johnson and later Koskenniemi using them to formalize the rule-based approach pioneered by Halle and (yes) Chomsky (well, not quite, but this is still the point of reference for rule-based phonology).

(I am a theoretical phonologist, but my colleagues who do actual NLP work of this type tell me that statistical methods aren't that great for the sort of work they do.)