No. The key concept for immersion is "willing suspension of disbelief". It comes from theatre and similar arts, where obvious inconsistencies will be ignored if they facilitate the telling of the story or would be impractical to eliminate. For instance, the characters will not usually acknowledge the audience, the stage will be a football field in one scene and utility closet in the next while remaining the same size, and characters whispering secrets can nonetheless be clearly heard from the back of the theatre. These are obvious inconsistencies, but the audience chooses to ignore them in order to enjoy the show.
In games, there will also be things that aren't realistic. AI, for example, is terrible. We forgive this, to an extent, because no game AI is believably human and is only as smart as humans in very specific cases. There are checkpoints everywhere and regenerating health because while the player might like to feel like a badass, he is usually not. It is not usually possible to go wherever we like because it would require the production of a huge amount of unnecessary content. We forgive these things, because they are necessary evils.
As long as a game is engaging enough, we will be immersed. Even a game like Doom, with horrible graphics, an excuse plot and fairly stupid enemies, can still be immersive because it is still fun in spite of that. You won't notice how unrealistic Doom is if you are focused on playing it.
Therefore, the most immersive perspective is simply the one that best facilitates play, which could even be top-down. A first person camera can actually break immersion in some cases, such as when platforming.