A theory

Throughout the whole film we see Freddy trying to get into Jesse's mind through his dreams and in fact he manages to mind control him before he makes his appearance in the real world. Freddy wasn't able to get into anyone else's dreams which raises the question what was so special about Jesse. His parents weren't involved in Freddy's murder after all.

The house was obviously tainted with Freddy's spirit after Nancy failed to kill him in the first film but at the same time Jesse must have been quite special to give Freddy such an upgrade. Not only did Freddy looks darker, scarier and more evil, he's now capable of controlling Jesse and even taking over his body in the real world. It's never mentioned that Freddy wanted to kill Jesse, in fact I think that Freddy was sympathetic towards him as Jesse was an outcast himself. He sure as hell is not your typical horror movie male protagonist, he's not manly enough, not too charming and he is vulnerable like a girl, all of that made him the perfect candidate to be use by Freddy the way he did. I think there might even be some dark past about Jesse that we are never shown on film.

And at last I think that Freddy's body never actually came out in the real world, it was always Jesse being mind controlled but we as viewers were shown Freddy to know that by this point Freddy had completely took over but the people at the pool still see Jesse having gone mad, while Jesse is in fact dreaming and being mind controlled. If you think about it Jesse and Freddy are never shown together in the real world and the kids at the pool don't even freak out as much as you would if such a demonic figure appeared in front of you. A guy even attempted to reason with him FFS!

If you put all the pieces together AOES 2 doesn't deviate from the rest of the franchise as much as people think. It surely takes a different approach but it can still belong in the same universe without plot holes. Underrated af.