I don't know how many here on Dave's are really that interested in Chomskyan linguistics - the problem is that it's never really been made to seem of absolutely crucial relevance to language teachers (many of whom teach ESL or EFL to boot).
Well, I myself don’t know if anyone at all on Dave’s is into Chomskyan stuff, but I also don’t know why Chomsky figures on threads.
Relevance to esl/efl? Yes and no. But is it all only about relevance? I think it’s a passion for language and related genres that initiates one into linguistics. I think most of us are here answering queries of learners only out of passion for the profession and the subject, and for some intellectual exchange of views. Curiosity. A person who deals in language might be curious as to how the hell it all works.
Relevance? Chomsky himself is modest in admitting that linguistic sciences are irrelevant and impractical for purposes of teaching. Regarding the difficulty in teaching target language to adults, Chomsky says “Use your common sense and use your experience and don’t listen too much to the scientists, unless you find that what they say is really of practical value and of assistance in understanding the problems you face, as sometimes it truly is”. Chomsky makes it explicit that those involved in teaching language should not take the sciences seriously, and he feels the ability to teach without much conscious awareness of what is being done is usually far more advanced than scientific knowledge. Modern linguistics, “are totally crazy and they may cause trouble.” He adds that modern linguistics has very little to contribute which is of practical value. “Language is not learnt. It grows in the mind. It is, thus, wrong to think that language is taught and misleading to think of it as being learnt.”
Inspite, linguistic theories are being “applied”. Chomskyan and even other models have central roles to play in computational linguistics, natural language processing, artificial intelligence. Chomskyan theories rely on native speaker’s intuitions to tell grammatical/ungrammatical sentences. In Chomskyan linguistics data are grammaticality judgements, a grammar is a description of the native speaker competence.
Theories should catch up with practice. Some recent research points to relevance. Among them, Pius ten Hacken (2002), in "Chomskyan Linguistics and the Sciences of Communication", Studies in communication Sciences 2/2:109-134, argues that Chomskyan linguistics is compatible with research in communication sciences and that the adoption of a Chomskyan perspective on language constitutes an attractive option.
M.C.Pennington in “Grammar and communication: New directions
in theory and practice” (Hinkel and Fotos, New Perspectives on Grammar Teaching in Second Language Classrooms) overviews Chomskyan minimalism, Brazil's incremental grammar, Clark's action grammar as alternative descriptions of English grammar to replace traditional approaches. Pennington argues that any new approach to pedagogical grammars should be collocational, constructive, contextual and contrastive.
An aside: I know of a teacher in India, who runs a language centre named after Chomsky and makes his students “acquire” English and not “learn” it.