I agree that the family is a unit and not a cluster of individuals, and that the health and wellbeing of each family member is important for the happiness of the family as a whole.
However, that includes the health and wellbeing of the kids. I believe in the saying that, as a parent, you are only ever as happy as your unhappiest child. And if your dc's mental health really suffers as a result of the move, that will impact on everyone.
Friends are at the centre of most teenagers' lives at that age. They are everything, and the idea of being moved away is inevitably going to be very challenging. That's not to say that they won't cope if there is no other option. The vast majority will adapt if they have to, and while they may hate it, it won't do them any harm to get used to the idea that change is a part of life. However, there will be a significant minority who really struggle and don't adapt, and you can't always tell who they are.
My dd is pretty confident and resilient, and she adapts well to change. I think she would be fine if we moved away... she makes friends easily etc. However, I know that she would be utterly devastated now if we moved her away from the friends and life that she loves. She would accept it if there was no choice for financial/health reasons, of course - she is old enough to understand. But it would be immensely distressing for her nonetheless, and I certainly wouldn't ever take that decision lightly.