I'm not saying that it's the only way to make a game immersive. What I'm saying is that it depends on the nature of the game. For instance the Total War games have a turn based strategic map that feature a large chunk of the world (typically Europe and the surrounding area).
Unlike Civ, where the battles are fought on the same map - keeping the game as one cohesive whole - the battles are real time tactical battles where you can control every aspect of the battle. Compared to Civ, that actually adds to the immersion despite completely changing the pace and nature of play.
Books. Books are a good example of what I'm talking about, actually. If a book switched from a third person style to first person and back again then yes, I think that would lessen the immersion. That is not to say that either style is superior (although I don't typically favour first person). It's simply that switching between styles can be detrimental, depending on the nature of the book.
I do agree with your point about developers thinking one approach is the best for any type of game. The thing that most bothers me about the upcoming XCOM is that the developers attempted to justify making it an FPS by saying 'well, that's what we make' /paraphrase. While the tactical sections could actually benefit from the perspective shift, they're producing the entire game in first person, which can only be detrimental to every other aspect of the game.
If the variety is well considered, like the old X-Com games, or indeed Total War then yes it is a good thing. But if it exists primarily due to technical limitations and the need to break up a game to fit within these constraints then it's not necessarily such a good thing. It could still be the best way to approach it, but the odds are against it.
With roleplaying games, where you're focussing on the story of one character, well it's the same as with literature, you don't want it broken up into a variety of styles. It's not necessary and can be damaging to immersion. Roleplaying games are pretty unique in that regard. It wouldn't matter so much if a strategy or action game was broken up into varous styles of play. But when you're a single character and shaping thier story the fragmentation is unwelcome.