Well, it sure doesn't seem like a PhD in business is for you. PhD is about becoming a researcher. And you don't seem to like it at all.
I agree that most people will not be interested in a research conclusion. Most people really aren't interested even in extremely important scientific issues, like evolution or relativity. You shouldn't do research because people are interested in it, but because YOU are interested in it.
I also don't see much of a point in doing research which will not make much a difference. So, I plan to conduct research about something I believe that WILL make a difference.
If you're doing research about something that no one cares about and will not make any difference, then I think you chose a poor research problem. Because research should be of interest for a few selected and important people. But that kind of research may take a lifetime, the PhD is just the beginning of it.
I'm about to start my PhD, and really I don't expect to deal only with pure theory only. I will work with real databases, from real companies, which faces real challenges. It's narrow? Maybe. But, then, nothing will prepare you to solve all the problems of the world, you gotta narrow it down. Be it an MBA or a PhD. PhD is narrower, but then you're expected to become one of the most knowledgeable persons of a given subject. It would be really impossible to be the most knowledgeable person of the world about a wide variety of subjects.
Social skills may not be the primary requirement for a PhD student, but it sure helps to be sucessful. Because working in collaboration may be important, maintaining good relationship with your advisor may be important, growing your network may be important, being able to present your work to an audience may be important. And it will be hard to do any of that without social skills.
I don't know what you call "higher level maths", but math is an important aspect of research in business. Even those concentrations related to psychology, for example, require a good math knowledge.
If a masters is already draining you out, a PhD is going to be much worse.
So, a PhD does not seem the right choice for you. But that doesn't mean an MBA is the right choice. You want to be a great executive, leader, manager, or something like that? If you don't, then MBA can also be a waste of time.