(It might be easier to understand the question if I phrase it this way from the start before reading the rest: What did states gain from spreading a particular religion?)
From what I've read, the many forms of paganism from the past tended to co-exist pretty well and they didn't seem to have power struggles among each other nor proselytization towards one another. Therefore, you'd think that to opportunistic or secular rulers, it would just be a subjective difference, like who prefers what color and so it would be unimportant; others could embrace the norm of tolerance they had grown up in.
But then there are instances where some religion (or sometimes irreligion, in more modern times) was promoted by the state - but why? What would it matter secularly/pragmatically if, for example, an animal was sacrificed to Hephaestus instead of Ares? Like Akhenaten's efforts for instance:
Certainly, as time drew on, he revised the names of the Aten, and other religious language, to increasingly exclude references to other gods; at some point, also, he embarked on the wide-scale erasure of traditional gods' names, especially those of Amun.
One way or another, all societies seem to have gone through some kind of religious unification though the past shows it to be unnecessary (the Greeks, Romans and Egyptians did well without it for a long time) and even today we can think of it this way ; if you're a Christian, the Hindus unified around Hinduism particularly for no apparent reason, if you're a Hindu, the Christians unified around Christianity particularly for no apparent reason. Others unified over what we think isn't true, and practices we think are unnecessary. Imagine if in Bhutan, over the next 30 years, the state put effort into stopping rock concerts and making rock music inaccessible on Youtube or something like that, while putting up ads for jazz and promoting jazz concerts, and that eventually the entire country stops listening to rock and listens to jazz or certain forms of it. Why would this matter to the state? To us it seems useless or just a subjective difference whether or not you would wake up at 7 am to burn frankincense on Saturdays or some other religious practice. Surely, the state or ruling party aren't harmed by this occurring on Saturdays rather than Wednesdays for example.
Why were societies artificially subjected to this homogenization of religious beliefs? Artificially meaning that believers weren't just left to change their beliefs over thousands of years as their convictions changed, but the societies or states would use propaganda, removal/addition of symbols/practices or buildings of some kinds, proselytize or incentivize to make the populace as polarized as possible. Was there an advantage to centralizing religion/religious beliefs in a society like this that could make sense of all these unifications from any perspective?
I removed the more detailed "discussion" about Akhenaten because it might have mislead as to what I was asking, but the point of it was to eliminate what I think would be "uninteresting", broad explanations. Like for example if I ask why the industrial revolution spread, you could say "Greed" or "Laziness" - and that would be true - but that could be said for so many things, the "why" of "Why was the wheel invented?" and "Why was the stock exchange invented?" are very different even if both are out of greed and/or laziness in the end.