I can actually. Plenty of studies on the topic have proven as much.
I guess it would depend on what you mean by immersion. You can be engrossed or immersed in a movie for example but it's not like YOU are part of the action, which is what they are trying to relay. To transport the player to that world psychologically, it is the best option outside of stuff like VR.
You kept mentioning "plenty of studies" but you didn't name any, so I checked on google and I picked a random one, it could be different from other ones. It's called "Immersion and Involvement in a 3D Training Environment: Experimenting different points of view", by Amon Rapp and Cristina Gena if anyone is interested.
As you say it depends on what you mean by immersion. FPP is more immersive as "it allows users to forget the mediation of the avatar" (I'm gonna put in quotation marks the things that I'm copying from the pdf) and gives you an idea of where things are supposed to be (for example if you are in FPP you know where your right arm and hand are supposed to be and if there is an object on your right you can feel it as if it's on your right, while this same process isn't as immediate in TPP, or at least that's what I understood). At the same time though, in FPP "users need some additional features when they are exploring a complex 3D world, especially when they do not know the environment", because a FPP doesn't give you awareness of the world around you, since you can only see in front of you. According to the article a map of the environment could help the user with orientation.
"So, even if in the video games world, as we have seen above, the most common interaction model for action games is the avatar in a TPP [1] and in virtual worlds like Second Life a TPP appears preferable [4], in virtual environments designed for training sessions that aim at preparing users to face with potentially dangerous situations, the best design solution is the FPP, since it produces a better sense of immersion and a deeper involvement, providing a better quality of personal experience that could improve the learning process and the training activities."
So this is the objective part, what comes next is subjective. Personally I think a game like this would fall in the same category as "action games" and "virtual worlds", for which the TPP is recommended, but others could say that they prefer "a better sense of immersion and deeper involvement" that apparently would be better for training sessions; but again, at this point it depends on what you prefer.
So, to summarize: if you mean "immertion" as "being the one who is doing things, instead of an avatar who does them for me" then you will want FPP, while if you intend it as "feeling part of the world around me" TPP is probably gonna be better for you.