I don’t really get the feeling that “I am in the movie,” I think if first person can move the camera in ways that feel organic with intricate animations it can be cool. One game I enjoyed that made the camera in first person move more dynamically was Breakdown on the Xbox and Mirror’s Edge was cool. For me, I get sort of the same level of immersion whether it’s first or third person, I just prefer third-person over first because it’s more appealing to see the character and action from that perspective.
I tried playing GTA 5 in first person and it felt crazy weird. It’s just better in third person and I think Indiana Jones could’ve done things in a hybrid fashion. Like the game is third person and if you need to solve puzzles you could go into first.