KB: And you are free to do that, but it isn't the logical necessity of the situation.
Moreover it is certainly a shaky assumption to assume that all campaigns have the same cosmology, and I should point out that even Greyhawk has large areas which don't adhere to your multicultural idea.
Assuming that at least some of the gods are rivals, why don't alliances (pantheons) form? Why do you not consider the group of gods favoring one race or another a pantheon which is the rival of other pantheons? If there are multiple gods over the sphere of say fire, why would one want to discourage the worship of another and monopolize fire worship in a particular area? If the ruling class of any area holds to some set of ideas, why wouldn't they want to outlaw opposing ideologies (good, evil, law, ect.)? If the gods of any area hold to a some set of ideas, why wouldn't they want to outlaw opposing ideologies? Why are gods of diverse opinions forming friendly concensuses? Why would their be evidence taboo's aren't necessary, given that they could literally be divinely enforced? Why wouldn't populaces form for historical reasons who worshiped only a small subset of Gods and refused the worship of others?
"Oh great Diana, if you will only save us from the ravenous maw of Xxichex, then we shall erect a great temple in your honor and make a great sacrifice and our children shall worship no other, nor offer sacrifices to no other, unto the thousandth generation, shall your name be venerated in Velidia..."
These are not 'irrelevant factors'. To me they are the natural result of assuming societies to be diverse and complex, and it takes an equally complex and special explanation to just write them off.
And while there may be answers to all these things, another DM can answer them completely differently. I just think you have chosen to make your game world multi-cultural for personal reasons, and I don't really feel like discussing the personal reasons why people do things.