For a majority of instances, I doth contest.
Open world multiplies playability directly proportional to how expansive the map is, how many different methods one is allowed to use in completing a task (I have seen compounds with three separate ways of breaking into them all with their own advantages,) and how hard the writers worked to make player decisions mean something.
On the last point - you mentioned that a player could kill everyone.
Yes... very true... and they could also COULD leave everyone alive. The player's CHOICE to kill everyone changes the dynamic of the continuing story. If the player does not like the effect of that route - they could load up a new game and take another route.
Concerning immersion: A linear game has conceptual walls. Wall within which the writer, designer, and producer expect the player to stay to allow the game to progress. The abrasive grinding of my face against that wall slowly chips away at the immersion that you speak of.
I think that my character would jump off the bridge into the water to escape his attackers. "No" says the level designer - the water is fake and there is an invisible wall. "No," says the writer, "your character is very brave and likes to kill people." "No." Says the producer, "You paid us $50 so we can tell YOU what happens next."
I fold my arms and tell them all that my character is a coward that wants to jump from a bridge into water - fake or not.
See the problem? My impression of who my character is doesn't mean anything unless the writer HAPPENS to agree with me.