The way I see it is, I'm engaging in a tradeoff I might very much make in real life, except instead of judging the physics of jumping a wide gap, or shooting a distant target, or how I understand how people respond to flattery, or whatever other real-world mechanics are in play, I am judging the mechanics that simulate/emulate/whatever-hot-button-verb-you-want-to-use those kinds of tradeoffs, and which simulate/etc. them so well that as a result I feel very much embedded and immersed in the situation, and I am absolutely, 100%, totally inhabiting my character's mental and emotional states in doing so. TTRPGs are neither reality nor larps, so something has to substitute for the various real-world systems at play. Otherwise I'd argue that by your standards, immersion in TTRPGs is simply impossible.
I mean, it isn't absolute. Nothing is. But let me try and illustrate the difference I am talking about.
The situation: a PC has run into an old rival and after some tense conversation, the player decides to engage in some violence.
Trad Game: Player says, "That's it! Eat steel!" Roll. Hit. Damage. Mechanics are involved, but they are pretty straight forward. GM: "NPC wipes the blood from his mouth, smiles ruefully, and says, 'Just remember, you started this.'"
Narrative Game: Player says, "That's it! Eat steel!" Roll. Dice come up with a success with a complication. The player says, "Okay, I guess I will hit him but he gets to hit me back?" Player 2 says, "Wait, it would be cool if you got your licks in but your sword got stuck in the table!" The GM says, "No, I think you hit him but he gets a chance to hit you back, Take2 harm."
That negotiation is where I think immersion takes the hit. Up until the time to adjudicate the die roll results, the immersion is equivalent. I'll even concede that based on building fiction previously, narrative games might even have better immersion in the lead up. But I think that once you ahve to put on the brakes to go through the process of determining what those dice results mean beyond simple algorithmic outcomes of smooth GM narration, immersion is broken.
Again, I am NOT saying it is any less fun or any less engaging or any less good. I am just asserting that the quality of immersion -- inhabiting the character inhabiting the world -- is reduced when you have to, as players and GMs, negotiate die rolls. As such, i think trad games with strong GM authority actually promote immersion over narrative games.