On the Cyrus Cylinder, arguably the first reciprocal commitment between a ruler and their people, Cyrus is portrayed as having been chosen by the chief Babylonian god Marduk to restore peace and order to the Babylonians.
The Mandate of Heaven, was a Chinese philosophy that there was a right of rebellion against rulers who were unjust, or in the face of famine flood and widespread poverty.
The Pax Romana was inaugurated by a ceremony by Emperor Augustus of Closing The Gates of Janus symbolising that Rome was at peace, and creation of the Ara Pacis, an altar to the Pax. The altar has a lower frieze depicting agricultural work meant to communicate the abundance and prosperity of the Peace. The monument and the significance of the Pax were the centrepiece of propaganda to ease the tensions around ending the Republic and formalising autocratic control, which had got Caesar assassinated. The concept led to many other examples of propaganda terms for justifying imperial control by peace, like the Pax Britannica.
What I think is interesting about these examples, is that they covered systems of absolute rule, but show a discourse engaging with justification to the ruled why they should accept a ruler and their system. These formal expectations of justification by peace and plenty also covered huge areas of the world, and vast spans of time.
Genghis Khan's rule was justified by him beating the other contenders for leadership, and uniting the tribes. In the face of two very cold winters and associated risk of starvation, he was able to secure fealty with the promise successful wars. It's interesting that while mainly known for vast destruction, his empire also secured what is called the Pax Mongolica, allowing the flourishing of trade, especially on the Silk Road. Trade generally produces far more wealth than conquest, and in the long run contentions between power blocks often come down to which has the stronger economy.
Religion has been a major source of state cohesion, like Pakistan meaning the "land of the spiritually pure and clean". Many states have been defined by and centred on commitment to religious rituals and traditions, not to delivery of peace or ptopserity. However, plagues and failed harvests were often interpreted as a state or ruler having lost favour with deity/ies, like the Plague of Thebes relating to the sins of Oeidipus, or the Black Death leading people to perform Bonfires of the Vanities.
Social Contract theory formalises the idea of consent by the governed to the government. For Hobbes it was the need above all for rule-of-law that forced people to accept an absolute monarchy forever, to avoid life being nasty brutish and short. For Rousseau who had a more positive picture of the State of Nature, it meant a more reciprocal obligation between ruled and rulers, creating a right to rebel against rule which no longer served a people. As Thomas Jefferson summarised it, "When injustice becomes law, resistance becomes duty."
So peace and prosperity are not the only modes of expectation from government, it may be the promise of war and conquest that brings people together though likely for hostorically short eras, or it may be religious rites although it can be argued these tacitly expect peace and prosperity for those 'right with the gods'.
Arguably the beginning of human cooperation into states, involves getting a group to risk death fighting to preserve a system of organisation. So there have to be benefits, materially or psycholigically at least for those committed to military service, which historically was the basis of citizenship. I would relate that bioligically, evolutionarily, to the expectation that descendents will be better off with the system, even if the 'ultimate sacrifice' is required.
So while peace and prosperity are not absolute expectations for all people in all times, the expectation of benefit (at very least to the elite) is the basis of human cooperation, which we now describe as the Social Contract. Wars consume vast resources, and lives, so peace and prosperity generally coincide. There needs to be a good reason for war, like a radical disagreement in world view, or explicit threats to those who will fight.
In short, yes I think Mises statement is justified.