If any part of a society is to be insured sustainability, then the entire society, taken as a living dynamic system, must have certain stability characteristics. This is not to say a sustainable society must be a static society, but there must be appropriate regulatory mechanisms that keep the various elements of society within some kind of balance and harmony. In primitive societies the regulatory mechanisms were natural and cultural. These cultural norms and economies evolved over time out of the necessity of societal survival. But such societies were relatively static, making stability easier to achieve.
Modern societies are highly dynamic, and achieving stability is therefore more difficult.
In dynamic systems, stability is achieved through feedback mechanisms. For example, a house is kept within a stable temperature range by means of a thermostat. In order for the thermostat to do its job the temperature sensor must be located in the house and it must be able to control the furnace. In general, a regulatory mechanism must be linked to that which is to be regulated, otherwise the system is unstable and runs out of control. What GDP measures is monetary transactions, not social well being.