That method (1) has the DM playing the role of the player by deciding for the player what their own character does and
If you want your character to take precise actions,
you must speak precisely. If you wish to retain agency,
be your own agent. If you act carelessly, how should anyone know that it wasn't intentional?
And sure, you
could play where the DM says:
"You open the door and see a 20x20 foot room. In the middle is a porcelain vase on top of a small stone pillar. None of your characters notice it without searching, but the pillar and vase are trapped with a contact poison. Also, there's a concealed panel in the floor by the wall, but again, you'd have to search to find it. What do you do?"
I know that my table would dislike that approach. The players would feel like that breaks immersion for them quite badly. They
want to be surprised or mistaken for their carelessness. It's a fundamental part of the game.
(2) potentially breaks "immersion" so the DM and player can hash out what the character is actually doing, after the player objects to the DM taking over their character for them. If you care about "no metagaming" and maintaining "immersion," how does this approach serve your goals?
Rewinding time a few seconds breaks immersion far less than telling the player that traps exist that their characters don't know about and then expecting the players to roleplay honestly. Yes, they
should be able to do that, but it makes roleplaying needlessly difficult. It also eliminates an intentional game feature: keeping player knowledge and character knowledge the same to enhance verisimilitude.
Like if the player says, "The key must be inside the vase. I run in and smash it with my club!" And the DM says, "Actually you fall into a concealed pit trap three steps into the room before you make it to the vase," I don't think that time rewind is actually breaking immersion. The character attempts to complete an intended action, and the game-world's reality intervenes in an unpleasant way. Indeed, the existence of reaction actions means this kind of temporal anomaly is literally a game mechanic for PCs and NPCs, making it unavoidable.
That's just my opinion,
but you don't need me to clarify that.
Reading the last few pages, I don't see you making any new points at all. At this point it feels like we've belabored the point well beyond critique. I think instead of continuing to claim problems with the methods we're saying work just fine for us, it's time for you to explain how you run it instead. You're clearly not making a convincing argument by just claiming our method is worse. You're just claiming it could be run differently, which isn't a particularly strong or enlightening counterpoint.