I remember reading something that, back in classic-era Who, someone (the showrunner, a writer...I don't remember the details there) had a "master plan" with the Seventh Doctor's plot-arc. Presumably it would be revealed that he was one of the founders of Time Lord society along with Omega and Rassilon; I believe a couple of hints as to this planned story-arc were included during the final classic-era Dalek story, with the Hand of Omega. I've read that it would have eventually also have the Doctor give Ace the option to become a Time Lord (somehow), and that his adventures with her during that last season or so were sort of "grooming" her for that possibility.
It sounded ambitious but unfortunately also incredibly convoluted, and I can't say it would've improved anything. I do prefer the mysterious nature of the Doctor; in fact, if it's simply left at him having been an "ordinary citizen" among his fellow Time Lords, I would find that preferable. The show (especially during the RTD era, but at most times during its entire run) has very much been about ordinary people finding inventive ways of displaying courage and heroism in the face of dangers and tyranny. So it would be entirely appropriate for the Doctor himself to have that very same background; it won't make him an epic-super-important-Time Lord figure, but since they're all gone anyway I don't see that it would be necessary to somehow distinguish his place in their society any more.
I don't think Moffat would bother with any of that storyline anyway, but I'm still anxious about what he has planned, because while his one-off contributions to the show have been excellent, he's been markedly poor in his long-arc planning and character backstory/development. I really hope that his resolution to this "first" "Doctor WHO?" question doesn't negatively impact or trivialize the series, is all.