If you hit an orc with the mace, you the player are not hitting the orc.
I am making a distinction between exerting power on the setting through your character (whether that be what your character says or does) and exerting power on the setting through your declarations as a player. In real life, I can say "I have a fort on the hill next to my house" all day long, but saying it doesn't make that fort exist. My memory of the fort is only valid if the hill and fort exist. The same in a setting. In a traditional style of play, the player asks the GM "is there a hill there"----the GM is the system for deterimining the objecting reality of the geography. Now you can play a different way. I am not saying playing differently is less fun, less immersive for you, or bad. I am saying if you allow the hill to exist because the player says, even if it is in character, "there are hills to the north", then that is distinct from how many on this thread play the game (and I would argue probably distinct from how most people play----but who knows, maybe that is changing).
I think that no matter what we're talking about, it's all through declarations as a player, right? That's all that is actually happening, whether it's the swing of an axe, or remembering a location, or trying to disarm a trap, or finding out the latest rumors.
I think that it's important to keep this in mind.
What you're advocating for is a mode of play where the vast majority of content is introduced by the GM. In this mode of play, what the players can declare is constrained by what has or has not been established, and with any unestablished factor going to the GM.
This is indeed a popular mode of play.
I think what's frustrating, is that you constantly site this mode as "normal" and "long established" and so on, which implies that any other approach is abnormal. The fact that you can do this, without seeming to even realize you are doing it, while also appealing to others to not place some objective value on their preferred approach, is a bit tough to take.
Anyone can play however they like, and there is no wrong way to play. But that doesn't mean every game allows the same amount of agency. There are mechanics and methods that allow for more or less agency.
Having the GM be the arbiter of almost all the fiction in the game is one method that tends to allow for less player agency. It's okay. This being a descriptor of a game is not the same as saying the game is bad or allows for less fun.
This is a very weird argument. The orc already was established as existing by the GM. And its death was contingent on a successful attack roll and doing the right amount damage. You didn't create a dead orc. You killed an orc that existed in the setting. The hill exists because you said it does. There is an obvious difference between these two things. If they feel the same to you, that is fine. I can't change that. But they don't feel at all the same to me.
So the distinction that seems most important to you seems to be the initial introduction of an element to the fiction. Does that seem right?
The GM should (in most cases) be the source of new fictional details. "There are hills north of the swamp!" The players are then free to go to the hills, or to avoid the hills, as they desire.
If a game allows the player some means to establish the hills.....what's the problem?
Can't a game do this? "I make a Wilderness check to see if I know where we are. If it's the Great Swamp, then Lothar knows the Iron Hills are to the north of us....." a successful Wilderness check means the player was right, and the PCs are now in the Great Swamp, and the Iron Hills are to the North.
This is a different approach than what many are used to, yes, but that doesn't mean it can't be suggested as a valid way to play, and as a method that will very likely increase player agency.
The whole fictional world doesn't come crashing down if someone besides the GM decides what's on the map.