The main issue with have Kylo be the killer of her parents doesn’t really help with anything in my mind personally.
His goal is to have Rey on his side. Would using the direction of “Oh yeah, I killed Han Solo, my father who you liked. Also, I tried to kill Luke Skywalker … but too bad he was a Force Hologram. Oh yeah, I killed your parents too. Wanna join me and make out?”
I just … don’t see how that helps with anything with whatever motivation the route a person wants to go.