I'm sorry, but the premise of this question seems flawed. Some variant of Chinese script is used by 1.3 billion people. Arabic scripts are used by about 600 million. Devanagari and Eastern Nagari, the two main (closely related) scripts of India have about 600 million users each. Slavic scripts about 250 million users.

In Muslim cultures, Arabic scripts became dominant. In the Chinese sphere of influence, some variant of Chinese. In the non-Greek Orthodox world, Cyrillic. In the Hindu (i.e. Sanskrit-dependent) world, Brahmi-derived scripts.

If there's a common denominator, it would be religion and holy scriptures, for which many scripts were originally devised. There really isn't anything special about the Latin alphabeth in this regard. Remember, Europe proper has about half as many inhabitants as India. It's not that big on a global scale.