Eh, I disagree with your premise. Immersion isn't just a matter of feeling like you're "in the game." I mean it's great when the controller seems to disappear, when you're no longer experiencing a game through that physical medium but simply having that direct contact, but it's far from the only way to immerse someone in an interactive experience.
Turn-based combat does not achieve the aforementioned direct experience, but it doesn't try to. Final Fantasy games, for instance, immerse the player in a complex world and mythology with interesting characters that make you want to understand it all. For that, more immersive combat is simply not required.
The other thing to keep in mind is that turn-based combat is not some uber-unrealistic thing that fails at simulating combat. We must remember that video games always, always, always attempt to emulate the experience, not clone it, because the latter simply is not possible. Even Call of Duty does that. Why? Because real life is not a game. Games need to construct themselves based on what makes for good, balanced mechanics before basing themselves on realism; that's why it's quicker to pull out a pistol, an entirely separate gun, than it is to reload a weapon, for instance, and that's in a game that strives for realism even to a fault. Heck, even Chess is a battle simulator, just governed by rules that may not be realistic, but are certainly balanced. Turn-based systems are simply gamified representations of combat, no less so than that of Battlefield 3, if a bit less realistic in some ways.
I think that is incredibly important to understand. Heck, no one complained about Puzzle Quest's combat being unrealistic, because it was freakin' brilliant, but as soon as the same type of game happens with actual characters fighting onscreen, it's unrealistic? We need to come to terms with the fact that video games are representations of real life, and are not intended to be carbon-copies of it, but to make balanced, well-designed systems out of it. And turn-based combat unquestionably accomplishes that goal.