To throw in a new point, the immersion of an FPS can also be reached by using PP effects; For example, Dead Space got that gory little effects on the cam (I think these are PP effects) when the player got hit; Gears of War does have that, too, when you use that sinister little saw.
What I'm trying to say is, when you loose immersion due to the natural differences between FPS and 3PS, you have to find different ways to create new!
If a door is locked, you have to open a window.