Minus you took it the wrong way: using an FPS game turned to TPS.
Use animations meant to be seen in TPS and turn it to FPS and it looks good.
Did you read the entirety of my post?
Specifically this bit:
You almost never implement your first person animations as if you're making a third person game and then just slap the player camera on top of the neck when you're done because the end result looks weird.
Chivalry is made with first person in mind. The first person animations are specifically made for first person. They did not use the 3rd person animations directly in first person in a game focused on first person. You may be thinking "why go through all the effort of remaking animations in first person" and the answer is: third person animations look weird in first person if you just "transplant" them directly.
It's like trying to make a car, a boat and a plane at the same time and the end result will be something that doesn't drive too well when compared to cars, doesn't fly too well when compared to planes and doesn't sail to well when compared to boats.
It does all 3 but it doesn't excel at any of them.
RDR2 is build primarily for third person and even then they don't reuse the same animations, they're edited.
I've dicked around with the perspective in RDR2 in my still ongoing multi hundred hour playthrough and the animations aren't 1:1. All of the 1st person animations are tweaked compared to their 3rd person counterparts (or even missing in some cases).
For example there is no first person animation for the protagonist with a rifle idle in their left hand like you have in third person and that could have easily been done if your theory of just reusing third person animations directly was true.
And to provide another example.
I don't know how familiar you are with Skyrim modding but between Oldrim and SkyrimSE we've had a few immersive first person camera mods (basically when you look down you can see your body). They're not trivial to make, they require a lot of reverse engineering and are typically implemented as script extender plugins and not normal mods because Skyrim simply wasn't built for such mods.
Although now that I think about it Joy Of Perspective was done through editing the first person skeleton I believe... yes, that's another thing, the two perspectives don't even use the same skeleton in Bethesda's games.
Some of them use the first person arms and render the body from the neck down minus ehad and arms. They do this by dynamically scaling some bones in the 3rd person skeleton (head, arms) basically making parts of your 3rd person character infinitely small so they don't overalp with the first person bits and then just render everything left. They do this because the third person attack animations involving your arms look weird in first person in Skyrim.
And some camera mods don't and as a result some attack animations looks plain bad and they also have to solve other issues like spinning attacks spinning your camera around.