I don’t think it was a question of “who trains him” so much as it was a question of “do we have him trained or not.”
I feel like she puts emphasis on Luke, they probably thought that Luke had the best chance of turning him away from the dark side. I don’t think training in itself would do that. I don’t know. I’m not sure if it matters though. I think the information in that line (whatever it implies) isn’t needed. And there being “Vader” in him is obvious anyway, Kylo is enough of a Vader Junior without it being spelled out.
I think the line about Luke is implying it was their only hope to control his power and stop him from turning to the dark.
The Vader line, at least in how I was using it in my dialog rearrangement, was a way for Han to express that it was a useless gesture to have Ben train with Luke, and that there is no saving him from this point forward.
Ah, yeah I see. I don’t think it should seem like Han has completely given up on Ben though.
I think Han giving up on ben and then later trying to redeem him when he sees him on SK base gives Han a more complex character arc than what he currently has.