Your goal as a nation, as a state, as a city, as an individual should never be to be a leader. Your goal is to advance your nation and your citizens in the pursuit of human advancement, achievement, and growth. You do not need to be a leader in order to do that.
The launch of the space race may have been rooted in competition but it ultimately led to the most significant advancements in society since the industrial revolution (if not more so). Ultimately, why are we looking to stabilize our relationships and tensions? As these basic needs of equality and calm are reached, the fused multinational brain power will let us, as humans, go beyond where we are today.
As a nation, our goal is reaching the stars because we are a tiny blue dot in the vast array of the solar system. Or else, you'll always gravitate towards on satisfying the unsatisfiable (pride, ego, rep, resources, etc.).