I think we would do the ancients a disservice treating the worship of the Greek gods as something uniform. It was anything but. At least during classic times, how it was during the bronze age I don't know as much about. If you go the wiki page of any Greek deity you will find information about local cults, epithets etc. It was varied and living. take for example the worship of our favorite partyboy Dionysus. Wine, tits and party right? Not completely. The partyboy association was a late addition to his myths, something that came about first in the post-Alexandian world. But for the Orphics he is one who can travel to and from the underworld.
But that is about the classic Greeks. When it comes to the Egyptians I am much less versed. But from my understanding of how connected the Egyptian priesthood was with politics I feel it was more centralized. Doctrine much more set in stone etc.
When it comes to drawing inspiration for polytheistic beliefs we don't have to look at ancient times. For example we have both Shinto and Hinduism being practised today. The feeling I get as someone who can barely consider themselves a layman is that there is very little internal religious conflict.
As for DnD the cleric section jumps between having god and gods in the flavour text indicating both is an option. But when it comes to actually creating the cleric there is the line
As you create a cleric, the most important question to consider is which deity to serve and what principles you want your character to embody.
Deity. Singular. So Dnd by default demands the cleric worships a sole deity. I mean they are a professional in the trade with insight into the mysteries of their god. How to worship them and how to receive miracles from them. This is also how it is in Runequest (and Glorantha), a dedicated priest almost always focuses on the worship of a single deity. Branching out is costly, both in time and in work for all the cults. But I am with you, if it makes sense for a cleric to be actively polytheistic then they should go for it.