Iirc, it wasn't just that as far as Star Trek goes. Iirc, most world governments and economic systems were destroyed, humanity was a mere fraction of its peak population. Humanity literally physically came together because it was necessary to rebuild.
Its one thing to have a common enemy/suffering without changing anything else as far as governments and social systems goes. It's completely different when you not only have the enemy/suffering but to also need to literally rebuild everything from scratch