A lot of companies today are searching for their purpose, they search for purpose because as work becomes more sophisticated and people become more skilled, people want a purpose.
So it only makes sense for governments or states to have a purpose as well.
It is important to understand that every organization has an generic purpose, that is the purpose to survive. So in lack of a better definition of a purpose that definition will always be stronger. if it is an economical organization (company) then its generic purpose will be profits, since the lack of profits (or losses) will cause the company to go bankrupt. The easiest purpose for a company would just to maximize profits, that purpose would be most efficient in private small companies where the owners/managers/employees are the same people. It cannot serve as a valuable purpose for anyone who does not share the profits of the company directly.
So if the first purpose of a state is to survive, it is an obvious conclusions that the state first needs to make sure it does not “loose” people or “power”, therefore it should defend it self. that is why the basics elements of most states ill be the army and police. The question remains what should be the purpose other than surviving as a state, and how well defined is it ? a purpose of gaining more geographic “power” would be colonizing, a purpose of more economic power would cause countries to enslave their citizens to work harder and harder (i.e – the western world).
The purpose of most people should be to create a better world for themselves and for everybody else (in that order). Specifically for states or governments i think the average longer life time of its population should probably be its main purpose, that would be a much better metric then GDP or population.
Who knows maybe our grandchildren will live till they are 200…