I don't think I think that.
It's more that I don't think that a human can be truly impartial. If I sat at the table of somebody who disagreed vociferously on my opinion of this topic, would I get a fair game? There would always be that question based on the outcome of the game. it might even be that the GM would over-compensate, and thus bias the game the other way.
The human brain's decision tree starts in the emotion chip of the brain. Everything after that is in support of that emotional decision. Thus, there is no guarantee that the impartial GM is actually impartial.
Since I don't think the GM is impartial and I don't see an absolute mathematically tested model to ensure he is reigned in, I see no point in pretending he is impartial. Since the GM has ultimate power (remember, no absolute mathematically proven model to bound his power), it would be an abuse of power and true imbalance to play as an adversarial role.
Sure, the GM's gotta try to be fair. Impartial? No way, he's a human and has just as much right to pursue his goals within the game as the players.
I don't believe that a DM must be an emotionless robotic calculator to run a fair game.
It is interesting that you mention that the DM has a right to pursue his goals within the game. The nature of those goals is of great importance.
If these goals are adversarial in nature, meaning the DM is trying to "win" through the use of some "rules" then he has already failed at running a fair game. The DM is the caretaker of everything in the game environment apart from the PC's. Not every part of that environment is going to be hostile to the PC's. Also consider that a campaign with any mystery or sense of wonder will feature elements that the players must discover. The DM is aware of these hidden rules and elements so playing
against the players is a pointless foregone conclusion.
The DM plays many roles. Some of those roles will involve portraying things that are hostile to the PC's. The role of Dungeon Master itself is
not such a role.
So what is the goal of the DM? Why even bother playing a game that you are not trying to win?
My personal answer to this is that the DM
isn't playing the game. He/she is
running the game that others play. The tradeoff for participating in a game one cannot win or lose is being privy to the whole picture and enjoying the action of the game as it unfolds. This isn't something that everyone finds fun and is one of the reasons there are far more players than (good) DM's.
The short version: If a DM tries to put a horse in the race, the game is already over.
Now is the GM a puppet master? I don't necesarily think that either. Sure, a DM is in position to manipulate the players, and what GM doesn't. But ultimately, the GM has a game because he delivers a great experience for the players. And that means it can't be against the players will. Not truly.
The DM has a playing group because he/she delivers an enjoyable experience. The group has a
game (or not) depending upon how they decide to spend thier time during that experience.
Death is of course a possibility from the PC's point of view. But this doesn't tell us that it has to be a possibility from the players'/metagame point of view. And we don't necessarily have to change genres (eg to super-heroes). There are fantasy-adventure RPGs where the action resolution mechanics mean that PC death is not really on the table (eg ICE's HARP, with its Fate Point rules - one Fate Point is enough to turn a killing blow into a merely serious one). D&D doesn't have quite that sort of action resolution option, but there are other ways of proceeding that are quite legal within the rules (eg 4e's "unconscious at zero hp" rule).
My answer to this is as simple as a Coke commercial: Ain't nothing like the real thing baby.
If the players are aware that character death is not likely then such knowledge will influence thier behavior in the game. Sooner or later it
will become a factor. Browse through all the "how do I stop the PC's from hacking into everything"/ " how do I get my players' characters to act like people" threads. Chances are high that these players are in campaigns that feature some sort of protagonist protection that they are exploiting for all it's worth.
Sure, but "creation and modification" is a long way from "possibillity of PC death as a result of random die rolls". In fact, in a game where (as a player) my main means of creating and modifying is by having my PC do things, than random chances of PC death might be seen as an obstacle to that creation.
Of course it's an obstacle.

A failure or setback is supposed to be an obstacle. PC death is simply the most severe of these.
Not always, of course - some games and playstyle make bringing in new PCs, or resurrecting dead ones, easy. Others do not. The link between PC death and deprotagonism is subtle. But it is not all one way. It is not inherently deprotagonising to take the possibility of PC death off the table. But of course it does depend on how that is done.
Players play to have fun. The concept of considering something like deprotagonism is anathema to our fun. Your mileage varies, and that is fine.
I've played lots of sessions of fantasy RPGs, and never once confronted the possibility of a character dying from a burst bladder (as did Tycho Brahe). That's predetermination of a sort. I don't think it's ever mattered, however. That's not the sort of possibility we want on the table (unless, maybe, we're playing F.A.T.A.L.). Is PC death an important possibility or not? That's what's up for grabs in different approaches to play - it can't just be assumed to be important for everyone.
I can't say that I have ever played anything like that either (unless it was on the Rolemaster tables and never came up

)
The possibility of PC death isn't a condition for every possible game but that has been covered.
Short answer - there can be other reasons to play RPGs besides winning/losing. One reason would be to create (pretty hackneyed and low-grade!) stories with friends. Why use dice and mechanics? Because they (i) create a framework in which to create stories, (ii) resolve issues about distribution of narrative power across participants, and (iii) interject randomness/novelty/tension etc.
Winning/losing is the difference between a game and storytelling. As for tension/randomness, it seems tension is a non-issue if there is nothing to be won or lost and randomness isn't really random if we mold what results we get into whatever we like.
The real question here is - do we mean "makes sense" in the gameworld, or "makes sense" in the real world at the gametable. I think you mean the former. I would agree with what you've said, but only if "make sense" has the latter meaning. If it would "make sense" at the game table for the PCs to be captured - because this is what the players want, to keep playing their PCs rather than having them be killed - then that is what I would prefer to do when GMing my group. It's my job, as GM, to then find a way - retconning if necessary - to make this make sense within the gameworld.
I agree. The real question of what makes sense depends on if the players want a game or to be the main characters in a story. Once that is agreed upon it becomes easier to decide what makes sense in various situations.