While I agree that in the future we should strive to achieve this level of cultural cohesion, we're currently at a point where the incentive to do these things is largely motivated by technological needs by developing countries. As a result these countries gain experience in these fields that makes their research more relevant.
The space race is over, but it happened because the two most technologically advanced nations were competing for dominance that would essentially earn them the "world champion" title. That need to win the title is how we all got to space in under a decade.
Now smaller nations are competing for third and fourth place, and that's creating a technological revolution for them right now.
So think more long term. We've always been on the same team, but these are pre-season practices where we're all split into subteams and pit against each other to determine the roster. USA and Russia are first string. China and India are competing for second string.
When the season starts and were all wearing the same colors; we'll be unstoppable.