It seems somewhat unlikely to me that doing things holistically as you're discussing is possible or even desirable. It's my understanding that the ancients considered the gods to have different forms for good reason, and these forms would be worshipped in different ways. Examples include Hermes and Hermes Kthonos, Zeus and Hades (they were considered to be one deity at one point, along with Poseidon). Celestial deities were prayed to with outstretched arms looking upward, and their offerings burnt and allowed to float into the sky. Meanwhile chthonic deities would be prayed to facing downward talking to the dirt, and their offerings buried.
So yes I would say this division is relatively universal for the ancients, and I wouldn't undo those developments without serious consideration. But then again, there is precedent for this kind of holistic reintegration in Serapis...