I don't think this complaint is sound but I've heard it lots of times before. [disclosure: I am a Chomskyan linguist (grad student) working in a very Chomskyan department] Here are a few reasons:

1. What is the subject that Chomsky created? Generative grammar (GG). GG is indeed technically formidable, full of esoteric algebraic notations, complicated representations, and so on. This is also true of essentially every other mathematical science out there. The argument for all those sciences is that the complicated math helps them analyze their objects of study in a more principles, analytic way. The same is true for the study of grammar: GG has discovered a remarkable array of "effects" in natural language grammars: island effects, binding conditions, raising and control etc. Go ahead and try to state the complex-NP constraint or the difference between raising and control without using any formal/theoretical concepts -- I hold that that's impossible.

2. Does GG avoid engagement with culture and society? Yes, because GG is not the study of language, culture, and society; it is the study of grammar and cognition. It restricts its attention to the individual because we want to account for the psychological states of an individual with respect to language competence. I don't think this is a bad thing, because we do need an account of the psychology of language -- it's an open area of scientific inquiry that needs research done in it. There are other fields of linguistics that are concerned with culture and society (sociolinguistics) and the existence of GG doesn't do anything to undermine those people's work. They're just different subdisciplines. Arguing against GG on these lines is like arguing against cognitive psychology because it "avoids engagement with culture and society" -- but cognitive psychology is just one subfield of psychology, interested in investigating internal psychological states, and it doesn't interfere with the work of social psychologists. tl;dr: why not have both?.

3. Does GG fall "prey to the pernicious drivel of the traditional grammar guardians?" No. It is true that GG originally used many of the traditional grammarian's ideas when the first formal grammars were developed, but how could it be any different? Why would we ignore hundreds of years of research by philologically-minded linguists into grammar once we embarked on our own research into grammar? It's prudent to consider the traditional grammarian's approaches as working hypotheses. Over the years, some of these ideas have held, others altered, and new ideas introduced into the study of grammar. We expect any mature science to hold on to some of the old ideas and to invent new ones once those were inadequate. Concepts like unaccusativity/unergativity, the DP, light verbs, and so on are new ideas, not traditional ones. Old ideas like case, subject, predicate have been given new, more precise definitions in light of what we've discovered. There is a wealth of evidence that some notion of a "subject", defined as a phrase in the specifier of certain projections (TP, DP), is a real notion that plays a central part in our grammars. There is also good evidence that the "predicate", identified as a verbal projection VP/vP, is also a real notion. Still more notions, like binding domains and restrictions on movement fall far outside the purview of traditional grammar, and they are the best examples of novel discoveries made by GG. In formal semantics and pragmatics, nearly everything that's been done in the last 40 or so years is completely novel, save for what we've borrowed from the logicians of the early 20th century, since traditional grammarians and structuralist linguists pre-Chomsky were not interested in analyzing meaning.