Many films use first person perspective, or perhaps we should call it direct character perspective although apparently the industry term is "subjective camera", where we are literally seeing through the eyes of the character. Films like Cloverfield and Blair Witch Project don't quite accomplish this as we are still seeing things from a camera which gets passed around. Movies like Doom or Iceman have brief sections which can be effective if used properly. Horror films and thrillers tend to use subjective camera quite a bit from the point of view of the killer or monster. I suppose that would technically be called second person perspective since the victim is supposed to be the center of our empathy while the killer is a force of antagonism. Seeing things from their perspective is not meant to garner empathy with the killer so much as provide a canny way to show the victim being stalked while not showing the killer at all.
Disallowing the video camera movies (Blair Witch, [rec], etc) there have been very few films made entirely or even with a significant portion of the film in subjective camera. 1947's Dark Passage had the first third in subjective camera because Bogart's character has plastic surgery at the end of the first act, so the subjective camera was a gimmick to keep the audience from seeing the pre-Bogart face. M*A*S*H aired "Point of View" in November of 1978 which depicted the show completely through the eyes of a wounded soldier. The Diving Bell and the Butterfly (Le scaphandre et le papillon) apparently has lengthy sections of this, but I have yet to see this film. I may remedy this shortly.
The only film I know that is nearly entirely in the subjective camera is 1947's Lady in the Lake which stars Robert Montgomery as Sam Spade. The entire film is seen from Spade's point of view save for three brief scenes-- at the beginning, about halfway through and at the end-- where Montgomery speaks directly into the camera to narrate the proceedings.
There may be other examples, but these are the ones of which I'm aware.
Now, my opinion on this technique, speaking not of the brief uses I list in the second paragraph but of doing this for the entirety of a film, I have to say: it is a hollow gimmick. That is all. And not a sustainable one, either. It does not work for a feature length film. Maybe for an hour long television episode ,like the M*A*S*H episode but only marginally. That episode was aired during the seventh season of M*A*S*H when the started eschewing comedy and even drama for outright experimental pieces, which I applaud just for at least trying something different on television (episode 195 "Dreams" was particularly interesting for my money)
The problem with the whole idea is that often this is employed to "put the audience into the character." Empathy for the character is a vital element in film and storytelling in general and forcing the perspective is assumed to make this more profound that standard camera work could. This is what the advertising for Lady in the Lake was saying. "MGM presents a Revolutionary motion picture; The most amazing since Talkies began!" Unfortunately, this is completely incorrect. Subjective camera does not increase character empathy or immersion in the film experience. It actually makes these things more difficult for reasons of which I am not sure.
I think that part of it is that from subjective camera, you really cannot see things very well, especially the point of view character. It's difficult to develop any emotional connection to something you cannot even see. Which is why you don't develop any emotional connection with Jason as you watch through his eyes as he stalks yet another victim. If you don't connect with the character, you don't care what happens to them.
Subjective camera also limits the more base methods a filmmaker can use to maintain interest, like shifting camera angles. These technique produce low-level engagement by virtue of showing us something different, even just the same thing from a different angle. It's an ancient survival trait and it's mostly absent in subjective camera, or at least can't be used as often.
Subjective camera does work in other media, like video games, because video games are interactive. The forced first person perspective (or is it really second person? Hmm...) is coupled with interactive methods and they work well. Motion pictures have no interactivity. Subjective camera is not more immersive than objective camera. It is less because it makes it even more clear than usually that you are just watching a movie. Let me see if I can explain my complex reasoning:
In film (and most other storytelling for that matter), there is a main character with whom the audience is supposed to empathize, to identify. In other words, if properly written, the audience should be thinking "If I were this guy who had lived that life and I now found myself in this situation, I would probably do what he's doing right now," or even better, "I hope I would do what he's doing right now."
I'm boiling down a large, hoity-toity writing concept that could take thousands of words to a few sentences, but hopefully I'm communicating it properly. Basically, if you've ever watched a movie and asked "why is that character doing that?" or "Why isn't the character doing this?' then you are dealing with a poorly-written film. Ideally, the character should take whatever action you would take, or hope you would take yourself if you ever found yourself in a similar situation. If that action is also unexpected, all the better. It's techniques like this (and others) that make a film compelling, that really put you into a character, their environment and situation, making a movie watching experience immersive.
Subjective camera short circuits this, or at least does not aide it. We don't get to see the character's facial expressions (hence why most actors hate wearing masks) so connecting emotionally is difficult if not impossible. But worse is that, unlike other movies where the audience can yell at the screen to tell the character what they should be doing, in subjective camera they "are" that character, yet they are not since they have no way to guide them. This breaks that movie watching spell even more than watching a character go into the door in the haunted house, because you are that character. Yet, obviously you are not since you have no say in what that character does.
I hope I made my position clear. If not, I can answer any questions as best I can.