I don't think I would be bothered by waking up male (in fact, I might quite like it), but that doesn't mean I'd make that claim for other people. Being disabled and having been seriously ill is part of a big bodily disconnect for me which it may not be for others.

"It wouldn't make any difference to the Doctor" isn't an argument I've seen, though I'm not really in the fandom at the moment - I've more often seen "it shouldn't make any difference to the show Doctor Who", but sadly, with Moffatt's current track record, I think it probably would.

Time Lords can canonically change physical sex between resurrections (don't know about gender) but I don't think that saying "it would be no different to the Doctor" is a particularly feminist argument. I think that "it might be no different to the Doctor" is fair, as is "it might be different". Either way, it's something I'd like to see. And changing sex without changing gender could be cool, too, though probably something I'd rather see in fic at the present time.