You are correct that the surviving religions, predominantly abrahamic and Hindu grew to dominance in the classical period. This is normally identified as the Axial Age that took neolithic myths and converted them into centralized systems with ethical and moral standards. This provided a much stronger set of tools for imperial growth and the integration of conquered populations.
This era lasted about 1,500 years until these religions began to break down. This was broadly the result of internal inconsistencies and growing failures of logic as education slowly spread. This produced simpler, mass religions with Islam replacing Christianity from Easter Europe to Southeast Asia, Mahayana Buddhism evolving in China and central Asia, and the Renaissance in western Europe leading directly to the Reformation. Obviously this was still primarily the means of justifying conquest and subjugation.
Interestingly there were two divergent trends historically. The movement of mass belief systems in the west and East Asia became more rational and more individualized religions while still being used for the justification of wars and conquest. Islam, as the most simplified of very late classical religions was the most suited to political control that allowed the more rational and individualized development to be eliminated in the harshest regions making the Arabic versions of this ironic remnants of an earlier age. We still see that today.
In short, where political systems evolved greater wealth and knowledge in the broader population, religion steadily lost power. The Scientific Revolution in the west eliminated religion as anything other than cultural rituals and traditions. This pattern has held true for two hundred years.
America is an aberration having retained religion as a political tool while it simply faded away in western Europe and east Asia with the rise of education and individual rights. Even so we are seeing the end of religion within the next twenty to thirty years at current rates of decline. At least 30% of those under 30 in America are atheists and roughly 50% of working scientists in America are also atheists. The majority of the rest have relatively little to do with religion but continue to follow it for social reasons.
In western Europe active religionists represent a stable group at about 10–15% of the population and that seems to be where America will go. The same is true in Japan where very few people consider themselves religious in any traditional form. While this is true it is confusing to those who follow traditional religions because because Japanese enjoy and use rituals from a variety of belief systems without regard for their origin. This is an accelerating movement as traditional religions are increasingly seen as irrelevant if not an actual social problem.
While religions are changing into cultural museums, a valid role for them to play, the nature of human spirituality is evolving just as rapidly. In most cases the rise of the non-religious is growing as people explore new or newer spiritual philosophies and tools to meet contemporary needs. Even in America variations on mindfulness and meditation partially or completely removed from their modern Buddhist origins are practiced extensively. This includes wide interest and involvement with Wicca and other pagan or animistic traditions that are focused on respect for all life and the planet that is now heavily threatened.
At the same time while traditional religions are declining, versions of Christianity that survive are effectively social aid, recreation, and community centers with no real restrictions. The rapid expansion of group and individual identity has changed human social needs.
And this is not new. It has been in process for the last two centuries.