From what I can see, it's essentially all about parenting and the fears associated with it. I can't find any evidence of this interpretation online, though. Pls check out my full interpretation and give me your own thoughts.
Great work! I mean, I was sold by the title alone, but the arguments themselves are very solid. Especially when taking SH3 into consideration.
The loss of innocence is a scary, but unavoidable thing. How it happens, and how a child can deal with that is reflected in who they are modeling. Heather had Harry, and Alessa had Dahlia. Despite being the same soul, in many ways, they became different people with different conclusions once their innocence was brutally stripped away from them. Heather chose life, and fought tooth and nail for it. Even though she lost the most important person to her, she was loved, she had someone to lose, someone who through his boundless love, showed her the worth of life, both her own and of life as a concept in general. Alessa, unloved, used, and isolated chose death. Sure, she was doing it for "the greater good", but so was Dahlia, in her own mind. Even while defying her evil mother, Alessa chose to become a sacrifice, a choice her mother made for her as well, seven years ago. Different ends, same means. She knew nothing but pain, and the fear of pain in turn became the fear of life, as per your thesis on the meaning of the opening line.
While I disagree that SH1 is Harry's nightmare, I do think that him and Alessa share a link. In a way, she is his daughter, and they both fear (her being harmed) and want (Harry to save her) the same thing. Which could explain his deeper connection to the otherworld.
SH1 is bold in its ambiguity, so a lot of it can only be discussed and analyzed by making a few leaps of faith, no one should be afraid to do that. And yeah, ultimately I'm of the mind that SH1, 3 (and 4) are "cult stories", about as much as SH2 is a "disease story". It's a lot deeper than that, and those games deserve to have their plots and characters looked at beyond the surface level, just like you did.
I genuinely hope to see more of your thoughts in the future.