This reminds me of a quote from Mark Cuban: “Unless you have a reliable, duplicatable, scalable and consistent way to bring potential customers in, you don’t have a business. You have a hobby!” I think it’s very similar in science. It’s difficult to argue that this is science because it seems impossible to design a repeatable experiment which yields the same outcome every time.
They (not necessarily all applying to this one) illustrate that: (A) This fucking cool thing happened. (B) This weird presentation (or lab finding, or imaging) turned out to be, we're pretty sure, X. (C) This weird presentation or case was successfully concluded with treatment X, with the caveat that, you know, we can't prove it was the treatment that did it.
When other docs are searching for "wtf is this weird presentation?", finding a case that shares other clinicians' reasoning and a possible diagnosis for that weird presentation is super helpful. Some things are too rare for your immediate colleagues to have much insight.
Case studies are professionals kibbitzing with one another, not science. They may give rise to science, as when an unconventional but logically sound therapy appears to have worked and prompts someone to test it in a proper trial.