Weird that you'd say neuroticism is the "only one that mattered". I'm more inclined to believe that for conscientiousness. I gather it's strongly correlated with life outcomes.
The remark was in the context of getting along with your teammates, which is why we went through those personality models in the first place.
Assuming we are avoiding extreme lack of conscientiousness, it is much easier to have the conversation with someone who has better emotional stability so that we can decide whether they can modify their natural inclinations.