I think there's a defensible position that some classes of immersion are incompatible with mechanics that can be viewed as "unavailable" on an in-character level. its just hard to talk about because there's at least two different threads of thought about what "immersion" means, and they aren't particularly compatible in their assumptions.
We hit those differences in a previous thread. It's an unhelpful shared use of a term in common.
I take immersion to be about experience of the world. So the player-as-subject-to-game is looking outward. They're not concerned if they like fancy hats, they're concerned if fancy hats are in fashion in Waterdeep. Typically this requires more work on the world itself, and you see people use the term consistency to describe the value they put on the world having a sort of independent reality. The fiction stands up, and continues to stand up, no matter who looks at it or from where. Critics might point to fruitless efforts at over-precision, and a paucity of human story.
On the other hand, I see many thinking of immersion as about in some sense becoming the character. Consistency in the price of fancy hats doesn't bother them, they're concerned for if their serious-minded paladin would ever really be seen about town in
that hat. And if they are, they're concerned for how that feels, how they will act, how others will react. I'm being flippant, but I hope this conveys a sense of thought about who the character is rather than where they are. Critics might point to nonsensical disconnects where things don't follow, and a paucity of wonder in the world around them.
In a way, this speaks to an old divide. Dualism and physicalism. World as subject. World as object. Some physicalist-minded persons will say that they don't believe in magic because the physical universe is so
magical. World informing human thought. Human thought determining world. Tolkien wrote about the wonder of exploring Middle Earth as a kind of geographer or historian. He may well have been an immersionist in the first sense. We really need different terms, because for me both are valid and they're not dichotomous. There's no reason the second kind of immersionist can't live in a world envisioned by the first kind. I'd go further and say that if they did, they'd discover even more possibilities for their preferred immersion.