Another point against mentioning Vader at the beginning is that there’s no reason to believe Rey would know of his immaculate conception, so it feels more like Kylo is talking to the audience rather than Rey, since he’s basically using Vader to explain the concept.
It wasn’t always like this. Initially we had something like the following:
“You were right. Your parents were nobody. No father conceived you.” (haha funny word play moment. This is all Rey says in TLJ: “They were nobody”.)
“Don’t!”
“You’re so much like my grandfather. So like Darth Vader…”
“I don’t want this!”
“…destined to rule”
“No!”
We’re probably never going to agree what a good characterization of her parents should look like, that’s why I’m leaning toward omitting them as much as possible.