I am not sure that's true - the power to do a thing does not imply the DM has a particular personal stake in how it turns out. It moves the DM to a role where, if he or she had a vested interest, he has nigh-infinite influence, true.
And, shouldn't the GM have a vested interest in providing an entertaining session?
Yes, but an entertaining session != particular game outcome.
If you are using a published module, that is true.
That is one area where my design method may differ from many other DMs. I design the situations and environments without a thought as to the player character capabilities. There will be traps where trap should be logically placed regardless of whether the group has a rogue. There will be undead where undead would be found regardless of whether the group has a cleric, etc. In short, I try to design the environment to fit its conception. It is the player's job to devise strategies to play to their strengths and minimise thier weaknesses.
I don't know about the rest of you GMs, but my players tend to wander off the beaten track, out into areas for which no design work has been done. I have to "wing it" every once in a while. I may have the most bare of notes, or nothing at all - there is no design to refer to. I may need to grab a beastie and throw it at the party. Now, what happens if I have over or underestimated the strength of that beastie?
Happens to me all the time. Usually the players rise to the occasion and gain ragging rights. Occasionally, the group devises a retreat. Very occasionally, the group suffers substantial losses and needs to regroup and recover. But, that simply moves the narrative in an unexpected but still plausible direction.
Or, let's say the GM did have time to do a really good design (when a major complaint of GMs is lack of prep time, I don't think it is a given, but for argument's sake) - even the guidelines in the DMG aren't perfect, and the GM is a human being, and there is no playtesting of what the GM bring to the table. What if the design isn't very good - maybe it is over- or under-powered. Either way can be a lot less than fun. Everyone at the table is stuck with that?
From my expereince, the majority of games that still receive comment 10-20 years later come from over/under-powered opposition. Those events can become the stuff of legend for the players. The fun for the players can come from the mix of casual steam-rolling the opposition through terror-stricken characters.
You mention the possibility of stealing someone's feeling of success. That's a possibility, but not a given - I'm pretty sure that if you press that all players feel the same way, you'll find sufficient pushback to prove it not generally true. The GM should know his or her players, right? Shouldn't the GM's knowledge of players trump your theoretical?
Which is why I qualified my comment by stating some player types. Certainly, there are player types that have no interest in what I'm discussing. There is no 'wrong' way to play other than using a way that violates the group's expectations. There are ways I like and there are ways I don't. There are game systems that better support one style than another. I pick the system that offers the appropriate narrative/collaborative control for the experience I want to achieve.
I'd counter with the idea that the design is done by a single person in whatever time he or she has, with no playtesting to speak of, and the results are highly subject to variation at runtime. At the table, the GM has loads of player feedback where he or she had none at the design stage.
The results aren't really subject to variation because the typical scenario is only used once by one group. Published work can often have huge variation across the gaming population, but that doesn't mean it failed -- just that the groups ended up telling wildly different stories with the same material.
If you mean the outcome can be wildly different than designer expecations, I think that's a feature not a flaw.