What are you trying to argue in the great-grandparent? What am I supposed to take from the black cloaks, aside from the fact that it makes Dementors look like Death? I can imagine that perhaps Rowling chose this appearance because it allowed a frightening reveal later on. But that reveal uses the words "rotting", "death" and "deathly". On our first sight of a Dementor she also compares it to something "dead" and "decayed". She did this because fear of death seems near as universal as you can get. Dementors' most feared ability, destruction of the soul, has the same explanation.

The parallels that MoR!Harry sees are real, and they exist because death is (widely held to be) bad.