I agree with your notion but I find it very hard to word how I feel about the entire thing. I’m guessing that it’s because I do not understand the philosophy as well as I should yet.
You have all kinds of philosophical theories that attempt to explain it. Emergence, illusionists, dualists, monists, panpsychism and souls. All of them require prior knowledge about physicalism, idealism and platonic forms. Existence as a predicate all that. It is like a massive bowl of spaghetti. If you want to take one string out you take 3 or 4 with it that need their own unentanglement. And you must do so while being consistent.
For example a physicalist who believes that everything in existence is explainable by some sort of mechanism can’t posit immaterial things that exist on their own in another realm. Which would mean that a person is either their body or the person emerges from the functions of the body. It is so deep and complex.
I have spoken to a whole lot of people who think that science in it’s objective ways can never solve subjectivity. It’s simply impossible by definition. I find myself leaning towards such an idea but what do I know. Reality is already quite absurd! I might have lead this down a rabbit trail though 
TLDR: I seem to intuitively agree that persons are more than the sum of their physical parts. Subjectivity from objectivity seems absurd and since we are, in my opinion, nowhere near explaining it in a way that does it justice requires us to take a leap of faith. I also agree that the cheer happenstance of such a rich social and cultural world coming into existence with pleasures and pains, happiness and anger seems to imply more than naturalism, a teleology, a God. But once again, people are prone to make mistakes.