Even in larps there's a gradient to immersion, and either way, such a thing must be acknowledged and accounted for, or problems are likely. Changing one's level of immersion is a skill, and it isn't one that's deliberately taught or supported in my limited experience larping. Again, I hear things are different in the nordic/jeepform community.Absolutely.
Hence - in the context of TTRPGing - when we're talking about a GM portraying NPCs, or when we're talking about players portraying their PCs interacting with on another, I think the idea of deciding simply by inhabiting the character starts to lose its purchase. We don't want people to storm away from the table, especially if they're our friends who have turned up to spend the afternoon hanging out with us! And so we don't set about inducing, in them, the sorts of emotions that would lead someone to storm out. Rather, we ask them to imagine that someone is trying to do that, and/or has done that, and then to author something in response.
And then there's the possibility of actually being yelled at, which I have seen in both larps and tabletop games. I've been luckier in my tabletop games, in that even in very heated exchanges, the people involved are capable of communicating at the same time that they are in fact playing a part. So somebody might get legitimately worked up in character, and slam the table or kick back their chair, but they don't actually leave the room (and the game). This is a side jaunt from where you're going, of course, but I figured it worth pointing out.But how to we decide what to ask them to imagine? Do they imagine someone yelling at them? Do they imagine someone yelling at them so hard they can't take it any more? Do they imagine someone yelling at them so hard they can't take it any more and storm off?
They aren't necessarily at odds, but I can see how a context switch can upset the mental state of inhabiting and emoting a character, and for some players that's a no-go. But again, changing one's level of immersion is a skill that can be developed, much like actors taking direction in between (and sometimes during!) takes. I will refrain from linking to the infamous Christian Bale rant, however.Most versions of D&D go as far as the first possibility: one participant is allowed to establish this person is yelling at this other person, but then whoever is in charge of that other person gets to decide the rest.
Burning Wheel goes as far as the second possibility: one participant is allowed to establish this person is yelling at this other person, and then if a check (Intimidate is the most obvious candidate) succeeds, the other person's controller has to roll a Steel check. Depending on how that ends up, the other person might find that their character is not able to take it any more! (But they still get to decide how they respond to the failed Steel check, from a limited menu of options.)
Marvel Heroic RP goes as far as the third possibility: one participant is allowed to establish this person is yelling at this other person, and then if a check succeeds might impose a Storm Off complication on the other character. How that resolves in the fiction will depend on the dice size of the complication, among other things, but the controller of the other character isn't allowed to just narrate fiction as if no such complication was part of it.
I don't think any of these approaches is at odds with inhabiting and emoting a character.

The nuts and bolts of a game mechanic dictating one's character's response, though, that's ultimately a player preference. If you really don't like it, you're not gonna enjoy games that do that very much. Me, I'm fine with it, as long as the mechanic allows results to be informed by my character's values & such.