It's truly interesting to me that people are so divided on this.
For some, FP perspective is absolutely essential for immersion - and for others, it apparently is completely unrelated.
It makes me wonder if we think of the same thing when we think about immersion.
I guess what makes us feel as if we're really present in the gameworld has a lot to do with how we approach games in general. I suppose my own way of approaching a game is less cerebral and more "visceral" - as in I like to start out with the notion of being within the gameworld and even playing something like an RTS or a 4X strategy game - I like to imagine I'm really some kind of general or leader.
In a game where I'm just one person in a world that's meant to be experienced as if I'm that person, I don't see any doubt whatsoever that the perspective is vital to that particular illusion.
In fact, if I hadn't heard from lots of people - lots of times - that they really don't find that perspective so important, I'd have assumed it was totally and completely universal. It's really strange that it isn't the case, and I'm trying hard to "get it" - I just can't.
I think it depends on the relative power of eyes vs imagination.
I can paint an infinitely more vivid world in my head reading a good book or playing a game with decent writing than even the most powerful graphics engine could ever provide. What I observe may be the photons from the graphics on the screen, but what I experience is the creation of my brain which takes those photons and wraps it up with sound, imagination and emotion to create immersion or the lack of it.
So for me I can get more immersed in a Spiderweb game with negligible graphics and good writing than I ever did in Oblivion. I think with Spiderweb type games the lack of graphics possibly even work in their favour, it forces my brain to kick in and actively imagine at which point it can take over. And Oblivion is to me a prime example of something with good graphics but poor world creation. I never cared about tamriel or my character, so why would I pause to take in the view? Might have looked pretty but I didn't give a shit about it. Oh wow, a gateway to hell threatening to unleash unspeakable horrors upon this village! Let's finish off my fedex quest first and I'll come back to it later if I remember, it'll still be there.
I think it also depends what people want from the protagonist. I don't try to be the character. There's no game where I've really thought that this avatar is me (but with l33t sk1llz & a massive sword!). So first person, third person, isometric, who cares. Do I care about this character's struggles, do the quests on the list mean anything more than an opportunity for some loot, do I want to find out what happens to the protagonist and the world? Those things matter for immersion, but i don't ever think of the character as being me so don't need to see things through their eyes.