What are the benefits of doing a PhD on a case study? As I review PhD positions available in my field (environmental engineering/sciences), it seems to me that some subjects are simply big case studies. I mean that the entire research is about applying an existing method to a new place or context rather than developing a new method.

Of course, since no place is truly unique, the method will have to be adapted to it and this might lead to a significant contribution to research. But still it leaves me with the open question of what is the benefit of such a PhD for the student's future career?

I would guess that doing a PhD on a case study rather than on fundamental research leads to better job perspective outside academia, for example as a consultant, but that might hinder your chances of doing an academic career. The problem is that with a BSc or MSc you can already do consulting, so such a PhD seems pretty useless. But maybe I'm missing something of the big picture, hence my question here

Finally, are such PhD offers common in academia in general or limited to some fields/geographical areas?
Case studies offer researchers the opportunities to dig deep into the rich details of the case.  In social science, this can frequently mean being able to answer "how" and "why" questions, use qualitative data, and generate rather than test theories.  I am not a physical scientist or engineer, but I imagine that similar principles apply:  the details of specific settings can be more informative than a more generic approach.

Case studies and quantitative/comparative studies are (in an ideal world) complementary to each other.  One tries to build up a deep understanding from looking carefully at a single (or smaller number of) cases, while the other seeks to establish generality, test theories, and (depending on the field) establish causation.

That said, in my experience (again, social science), the communities of scholars who work on case studies are frequently relatively disconnected from the communities of scholars who do statistical/quantitative work.  When choosing your career path, be sure to think about which community you will be happiest in.