Ignoring the bit beforehand (which, though I understand your intent, I found to be a rather rude addition), I think your theory is super interesting! O:
Since I haven't read Sinbad yet (though I probably will while we wait for new chapters of Magi), my thought was this:
Given that every Djinn is the representative/chief of each of the non-human races from Alma Torran, it seemed to me that perhaps being Assimilated by your Vessel means that you become part of that Djinn's respective race. I'm not exactly sure how that fits for every Djinn's Household (mostly for Sinbad and the generals at least, since I'm not exactly sure who's which one, again because I have yet to read Sinbad), but it seems a very plausible idea to me.
I'm not trying to say my theory is any more correct, but that was my thought on it. I can't wait to see what we learn about this concept as the manga progresses!!