Yes! Agreed! I like your idea! I think the only two Links that usually reincarnate are usually the Hero of Time and the Hero of Legend! Like for example, the Hero of Legend from TP could be a reincarnation of the Hero of Legend from SS. And the Hero of Time from OoT could be a reincarnation of a...
I don't think the Spirit of the Hero is supposed to be literal. There's proof that it isn't literal in like two Zelda games. That being TP (Hero's Shade) and ALBW (Gramps AKA Old Man ALttP Link). Why people keep believing that the Hero's Spirit is a literal thing, I don't know.