In this episode, "The Doctor" is reprogrammed to "forget" that he saved Ensign Harry Kim's life rather than someone it didn't really know or consider a "friend." And it has problems justifying this. You'd think it got into an argument with Kirk or something...

Anyway, "The Doctor" is supposedly overwrought with guilt over saving "a friend" rather than "a stranger."

But wouldn't it be relevant that Kim's role was more important to the ship, their mission, and their survival?

I can only think of one "justification" for the way it was written, the good old Because Drama.