First, as they emphasize, correctly IMO, what made the Vergnaud theory so interesting as regards explanatory adequacy was that it was not signaled by surface features of DPs in some many languages (e.g. English and Chinese). In other words, it was not WYSIWYG. If it held then it could not be reasonably acquired simply by tracking surface morphology. This is what made it a UG candidate and why it bore on issues of explanatory adequacy. In other words, it was a nice example of PoS thinking: you know it despite no PLD to motivate it, hence it is part of FL/UG. Again, it is the absence of surface reflexes of the principle that made it interesting. As B&U puts it:
Deep down, case is compelling because linguistics has become a part of the Galilean undertaking, a way of explaining what is visible by an appeal to what is not.Not being "visible" is the key here.
Second, B&U notes how P&P models were influenced by the work of Monod and Jacob on the operon. Indeed, I would go further: the kind of work that microbiologists were doing were taken to serve as good models of how work on language could proceed and Case theory as Vergnaud envisaged this was a nice example of the thinking. Here's what I mean.
The operon was discovered by research on very simple bacteria and the supposition was made that how it worked there was how it worked everywhere. It's logic extends from bacteria to butterflies, chickens, lions, whales, worms etc. In other words, reasoning based on a very simple organism was taken to illuminate how far different organisms organized their microbiology. And all of this without replicating the work on butterflies, mice, whales etc. This reasoning as applied to linguistics allows inferences from the intensive study of one language to prima facie apply to all. Indeed, the PoS argument licenses this kind of inference which is why it is such an interesting and powerful form of argument.
Why do I mention this? Because linguists nowadays don't really believe this. Evidence that we don't can be seen in our reactions to critics (like Everett, Evans, Wolfe, Tomasello, etc.). A staple of GG criticism is that it is English centric. The supposition behind this criticism is that one cannot legitimately say anything about FL/UG based on the study of a smattering of languages. To talk about FL/UG responsibly requires studying a broad swath of different languages for only in so doing is one licensed to make universal inferences. We reply to the critics by noting how much current linguistic work is typological and cross linguistic and that so many people are working on so many different kinds of languages. But why is this our only retort. Why not say that one can gain terrific insight into FL/UG by studying a single language? Why the requirement that any claim be founded on masses of cross linguistic investigation?
Note that this is exactly what Monod and Jacob did not do. Nor do microbiologists do so today. Microbiologists study a handful of model organisms and from these we infer laws of biology. That is deemed ok in biology but not linguistics. Why? Why do linguists presuppose that only the extensive study of a wide number of different languages will allow insight into FL/UG? It's not the history of the field, so far as I can tell.
B&U shows how classical case theory arose. Similar stories can be told for virtually every other non-trivial theory within linguistics. It arose not via the study of lots of languages but by trying to understand simple facts within a small number in some deep way. This is how bounding theory arose, the ECP, binding and more. So why the presupposition (visible in the replies we give to our critics that we do, really really do, study more than just English) that cross linguistic typological investigations are the only sure way to investigate FL/UG?
I think that I know one answer: we don't really know much about FL/UG. In other words, many linguists will reply that our claims are weak. I don't buy this. But if you do then it is not clear why GGs critics upset you with their claims. Is it that they are saying out loud what you believe but don't think should be shared in polite company?