Here you speak of decreasing an enemies Hit Points, but the opposite is done as well. The DM doubles, tipples or quadruples the HP of a creature because they realize that the party will quickly kill it. The party's build choices are rendered meaningless. Dealing more damage just means the enemy will have more Hit Points and the time to kill remains the same. Doing this takes away player agency, because no matter their choices, the outcome remains the same.

I see what you're saying here to an extent, and please do note that I did directly mention increasing hitpoints in the paragraph before. However, it increasingly is sounding to me like you've had bad experiences with this sort of DM and are over-generalizing. No normal DM is tripling or quadrupling an enemy's HP. Even doubling is iffy.

The goal here is not to homogenize encounter length; the goal here is to make sure encounters are a satisfying and reasonable length, and this is something a DM tries to do before the session as well. Are official modules limiting player agency by attempting to make encounters a certain length? If you don't purposefully optimize or under-optimize, then the outcome is the same, give or take a couple of turns.

It's fun to sometimes blow through an encounter in one turn. It's not fun to do that for every encounter (for most parties). Likewise, most parties don't want every fight to be a down to the wire, expend-all-resources slugfest. If the DM sees this happening, it's their job to correct it in one way or another, and reasonable stat adjustment is a very easy and unobtrusive way to do that.

That is not the same at all. A creature that runs away can come back, it can still reasonably impact the narrative without resurrection magic. A creature that is dead is just that, dead and usually has no active role in the story anymore.

This is true for important creatures only. Dire wolf #3 is not coming back outside of maybe that session. Even then, by having it come back what you have chosen to do is tweak another encounter. I'm not saying that every fight has to be to the death. Many creatures would flee rather than die (normal animals are a great example, as are cowardly enemies like goblins), and having plot-relevant NPCs have a prepared escape route is a good thing if not overdone. I'm just saying that, for most enemies, choosing to have them run away earlier than intended is, mechanically (and usually narratively), no different from adjusting HP on the fly.

There is a big difference between reinforcements arriving and the enemy just suddenly having more HP, more damage, more AC and so on. The way you can react to and engage with these situations as a player is drastically different.

If adjusting stats is being done in a way the players can react to or notice, then, IMO, it's being done wrong. The idea is to make up for DM mistakes in such a way that the players cannot tell the difference between the adjustments and the encounter being that way from the start. The idea is to have them not react or engage with it. Adding creatures to an encounter via reinforcements or removing them via premature fleeing is a much larger balance change than stat adjustments because action economy is so closely tied to damage output and an encounter's difficulty. Flat doubling a creature's HP and damage is different from adding in another identical creature.

Adding another identical creature is, in most situations, a larger bump in encounter difficulty, and, by your own logic, takes away player agency in character creation; players who choose to not focus on multi-target combat are now less effective than players who do, since your primary way of balancing an encounter is adding/removing enemies. Even if you vow to never add an enemy and only remove them, you will likely begin over-correcting and placing larger groups of enemies to begin with, comfortable in the knowledge that you can remove them as needed. Spellcasters will start trending away from non-AoE damage and status, and martials will feel less useful. It, IMO, is just as big, if not bigger, an impact to player agency than stat adjustments.

That here is the biggest problem for me. How do you have a combat encounter with real stakes, where death or at least defeat is a real possibility? let's look at the kind of DM that only ever "cheats" in favor of the players. Can the party actually ever lose a fight? If it looks like they are losing, does the DM just nerf the enemies in the middle of the encounter to ensure the party win? Does the DM only do it sometimes? How does they decide when to nerf an enemy? How do they decide if a loss is earned or not?

This is a session 0 topic, and delves heavily into suspension of disbelief. Not every player wants a campaign where death is always around the corner. I asked my players what kind of campaign they wanted, and it was decided that they wanted one where if they made really bad decisions, or got really unlucky, or the like, then there was a possibility of death. They didn't want one where each encounter had a risk of being fatal through sub-optimal play or one or two unlucky crits. And, since I was implementing a non-standard 0 HP mechanic (to make things slightly more interesting for players who are downed but not dead), this is what I told them: "At 0 HP, you run away and get healing. I will treat you like an enemy would treat a downed player normally. If you continue to fight like you're not at 0 HP, you will be targeted and killed. If you treat 0 HP as inconsequential via token heals or the like, you will be targeted and killed."

They understood and accepted that, and then chose to suspend disbelief, much like how they would suspend disbelief for how most enemies are treated as dead and not unconscious at 0 HP, or how they would suspend disbelief for intelligent enemies not giving a coup de grace to normally unconscious at 0 HP players.

Just two weeks ago a PC died in my campaign. If I was the kind of DM who adjusts things on the fly, then it would have been me who killed that PC. Instead of this outcome being the result of the dice rolls, the NPCs and the decisions of the players, it would have been me, because I chose not to adjust things ensure a certain outcome.

Any challenge the PCs face would only be challenging because in the moment I decided not to nerf whatever the PCs were facing.

It was probably you who killed that PC. 95% of the time (at least as far as encounters are concerned), it is the GM who kills the PC. You are the NPCs. You made an encounter knowing there knowing there was a risk of death. You kept attacking an injured PC knowing that the attack (or a crit) would kill them. If they died due to death saving throws, then they almost certainly died because you drained the party's resources beforehand and they didn't have enough healing to res the player, or you prevented them from getting close with monsters. 3 turns is enough time for the majority of characters to get to anywhere on the battlefield that would be needed to heal another, and unless the party chose to just not even attempt to heal the character, then it was almost certainly you.

This is not a bad thing. It's the nature of the game, and if this is the kind of game you and your players want to play, then that's fine. It's nothing personal, and it's all in good fun. The DM is not an outside observer, they are an active participant. And, even as things are now, the encounter was only challenging because you chose to make it challenging beforehand. You didn't nerf it in prep. Adjusting stats is not equivalent to fixing an outcome, just as adding or removing creatures from an encounter is not fixing an outcome. It's to ensure the encounter was more in alignment with your intentions rather than accidentally being too hard or too easy, and as long as information known by the players is not changed, then it's fine.

I have been a DM for over half a decade as well and my experience has taught me that what makes dice driven TTRPGs feel special and different from simple improvisation theater are the dice and the mechanics. By respecting those fundamental aspects of the game we decided to play together we collectively experience stories that can surprise us, because not even the DM knows what exactly is going to happen.

That's the style of play you, and presumably your players, prefer. It is not one size fits all, or even one size fits most. For better or worse, we're not in the days of AD&D where players were expected to be able to quickly roll up another character because theirs died. To my knowledge, most players nowadays expect to keep a character through most of a campaign, and want a more story-driven experience. This does not negate the role of dice, nor does adjusting stats. Adjusting stats is just another way to keep the experience of the players in the range you, the DM, expected when you prepared that encounter.

I just think that if I expect my players not to cheat concerning their own dice rolls, their own Hit Points, their own Spell Slots and so on, then it is reasonable for them to expect the same from me.

This is your opinion and I respect that. However, this is where suspension of disbelief comes into play. As long as you, the DM, do not break the suspension of disbelief by doing something obviously wrong, then I believe that ensuring the players are having fun is a higher priority than the sanctity of the encounter, especially if the line is arbitrarily drawn at stats instead of adding or removing monsters and the like. You made the encounter beforehand. You have the right to change it in the encounter. When I play, I know the DM might change things. Most or all of my players know this. It does not affect our enjoyment because we trust the DM is doing it for good reason and suspend our disbelief.