LostSoul
Adventurer
I don't think I'm a "deep immersionist", so maybe this is wrong. But this is my take:
In deep immersion, you feel what the character feels. If the PC is afraid, so are you. If you're not afraid and the PC is, then there's an issue. Anything that disrupts that one-to-one relationship between your feelings and the PC's is ruinous to the game.
Come and Get It - or even Serpent Steel Strike - is strange to you, because if you did it once, you feel like you should be able to do it again, given the same stimuli (which you and the character are experiencing together). If you can't, that immediately breaks your immersion, which is why you're there to begin with. I would imagine that systems that have this possibility would look unsatisfying to you, and if they exist throughout the text instead of in isolated incidences, then you're not going to look on that system as one you want to play.
To be clear: I've never particularly valued this in RPGs. I like to get emotionally invested, but as a player, not as a PC - otherwise I'd never be able to play the PCs that I do. (My PCs do things that I would never do.) I want RPGs to challenge me as a player, emotionally or intellectually, but I don't feel the need to connect one-to-one with my PC in order to do that.
edit: What I want from immersion - what I think of immersion - is the ability to picture the scene in my mind's eye, and leverage what I see into mechanical resolution. I don't need to be emotionally connected to my PC; I need to be emotionally or intellectually connected to the decisions I, as a player, have to make, but those don't necessarily have to be the same ones my PC is making.