Then they could have actually taken advantage of the fact that everyone had their own camera.

It does not dispense with the pretense at all: the film claims to be assembled from found documentary footage in the prologue (and then proceeds to shoot in a narrative style), and relies heavily on the gimmick of the first-person cameras.

A New Beginning is great because it attempts to return to the original formula in which the identity of the killer is a mystery.

I do not think Freddy's Revenge breaks the rules of the first film. (I make a point to say, "first film," because Freddy's Revenge cannot be expected to abide by the rules established in the films that come after itself.)