I think you're both right. There seems to be a lot of crossing back and forth between acting in musicals and acting in straight plays, more than before. I don't think performers are as pigeonholed as perhaps they once were.
I also think that some of the game of getting nominated has to do with exceeding expectations. Glenda Jackson IMO is a good example. Part of the issue with her King Lear is that it wasn't quite as good as we hoped it would be, because we knew how great she could be from Three Tall Women. The novelty factor was no longer there, either. If Three Tall Women had never existed and her Broadway return was in King Lear, she would have been nominated (and perhaps won). After The Producers, Nathan Lane appeared in six consecutive Broadway shows without getting nominated, even though he gave several nomination-worthy performances IMO.
I think the novelty of an actor surprisingly revealing he or she can sing can help secure a nomination (eg, Martha Plimpton in Pal Joey, and dare I say Anne Hathaway in Les Mis). And an actor known for musicals who shows that he or she has dramatic chops without the distraction of singing and dancing can help. That's not to say that such actors shouldn't have been nominated, but who gets nominated and who doesn't is a game that doesn't always correlate with who would be nominated in a perfect world. (Not that such a world exists for such a subjective issue, anyway)