>>18066096 (OP)
It wasn't really a cope, it was downstream of how the Romans and Greek philosophers viewed the Gods.
I'll focus on two ways here that are most interesting, to me.
The first is that Greek philosophers (meaning here people that followed the cults of the pre-socratics and later platonists or neopythagoreans) had a view that the Gods were abstract and representations of natural forces but couldn't be personified like traditional myths would usually do.
Xenophanes, for example, from a very early date, quipped that if cows had hands, they'd paint the Gods to look like cows. He also said that divine power all traced back to a centralized single source that was basically unknowable, eternal, and wholly good. And its operations were the natural laws of the universe, not divine intervention or magic. And later Plato and Aristotle would develop this further. Even in some cases saying that Homer and Hesiod should be censored because they contained lies about the Gods doing bad things.
In this lens, what people call their individual Gods is irrelevant, because they're all foolish anthropomorphizations of divine cosmic and natural forces. One archetype, projected on some aspect of this single God, is basically the same as any other similar archetype. Its all just the human perception.
From the Roman side, there was this view that the Gods were basically very distant and more forces of nature than people.
The Romans didn't really have myths about their Gods doing things. Most of those actually came from later interactions with the Greeks. The Gods were forces of power in the universe that controlled everything and were owed respect and worship. But they didn't really interact with humans directly or engage in drama.
In this, it became common for Romans to gloss over differences in specifics between groups of Gods, because to them those specifics were unimportant. The overall archetype mattered the most according to what category of cosmic forces it fit with.