Interesting theory. As a fan of the slasher genre, I think it's pretty well explained about what a slasher is. Someone who died a wrongful death and has come back filled with rage, partly because of neglecting, (Friday the 13th) Jason Voorhees supposedly drowned, but in the sequel, it was explained, his body was never found. He was still living, yet he had a force in him that went off the moment he seen his vengeful mother decapitated which by all means, she did not come back as a slasher. Jason kept coming back because he supposedly died a wrongful death, only he didn't, he had rage in him that kept him from really dying.
There has been a final boy if you will, in Tommy Jarvis, the one who killed Jason, only haunted by his visions of Jason still being alive, he went ahead and brought him back to life (Friday the 13th Part 6 Jason Lives) He's been in mental ward after mental ward. He was able to put Jason in his supposed resting place, back in Crystal Lake.
Freddy Krueger well he's just plain evil, he's driven by the power of Dream Demons.
Victor Crowley, he was struck in the face with a hatchet in Adam Green's slasher film Hatchet. He was another tragic figure.
I guess it depends on the type of story. If it's just a serial killer going around and killing people, that's it, it's just a serial killer. There's so much material out there on how Slashers which are called Revenants, exist and what makes them what they are.