I am thinking of doing an EdD and in preparation have taken part in a couple of MOOCs for research methods. They delved deeply into the history of science, beginning with ancient philosophy. While interesting, it was a lot to digest and it left me wondering how broad my knowledge would have to be for doctoral studies. I could see the point of giving some background to how research has come to be, and also insights to the different research methods and approaches, but I wonder how much I would be expected to 'know' or carry round in my head so the information is on-demand.
Does this query make sense? If I do doctoral studies, should I expect to also know a lot about philosophy, politics, history etc (as the content of these courses suggest)?

It's great to have a general awareness of these things, but generally no, you need to be a specialise in your subject area, not the whole of learned society, so don't worry!

As a social scientist you would be expected to be able to give an account of the ontological and epistemological choices that underpin your work, so to some extent yes, you do need to know this stuff. On the other hand, a friend who did an EdD told me that the taught portion of the course was much more applied and specific to education, than the abstract research methods training the social sciences PhD students were getting. And of course the shorter EdD thesis means that there's limited space for those sort of chapters. If you're doing an EdD to try to move into academia though you'd probably need to take all that much more seriously though, judging by the sorts of articles our education faculty produce!

Even though you will specialise during your PhD, you certainly will be expected to develop a broader knowledge of relevant material as well. Speak to your supervisor about this and they will advise. Oh and expect to go through your entire PhD feeling you are not up to date. I think the majority of us felt that.