In my handful of interdisciplinary forays (all within social science), I've actually been struck by how different the fields can be, particularly in regards to the assumptions that are easily digested. In one example I found economists and sociologists were accomplishing the exact same thing using a completely different method, and no one in either field seems to have any idea why anyone in the other field does it that way.
There is also the issue of learning the specific research skills used in a given field. The skills I've learned as an economist are not the same skills learned by someone studying education. Even within the field of economics there are divisions with stark differences in skills, micro vs macro, empirical vs theoretical, and so on, that would make it very difficult to move between them as a researcher. That would likely be greatly compounded going to entirely different fields, even though all of the fields rely on "general research skills".
There's also a huge signaling aspect. You mentioned finance; this is a competitive area, and jobs will always have more applicants than openings. Someone with a finance degree has a leg up on someone with, say, an economics degree, while someone with an economics degree may have a leg up on someone with a business or statistics degree, while those researchers would be ahead of someone with a degree in education. I'm sure you can extend that chain if desired.
So in short, yes, it absolutely matters what your PhD is in. That doesn't mean you can't be an interdisciplinary researcher, particularly once you're tenured somewhere, or that it's impossible to switch to related but different fields, but your degree should be in your primary interest.