Thing is, it's not natural at all in Civ6. You have to search, tamper, guess, until you are ready to post that video on youtube. You have far too many bonuses "pools" you can toy with and are disconnected (apparently) from each others.
You have what :
- Civ uniques
- Leaders uniques
- Pantheons
- Religions
- techs
- social tree
- governments
- policy cards
- Allied city-States
- era (dedications)
- governors
- secret societies
etc.
All those to pick up in a generally silly-long list of choices that you have to read (and remember preferably) before picking up one choice. It's ridiculously overwhelming. Nearly unplayable. So yes, it would be good that some effects to be unified under the banner of one, single rather bigger effect directed towards one aspect of the game.
For example, one could drastically reduce the list of pantheons and the like you have to choose, maybe by tying them to your starting location. Pantheons themselves could be semi-random, tied to your starting location but automatic. (not choosed by the player)
The ones who would be in charge here would be rather your population, or a council of wisemen. You may even be able to elect the guys in that council, to influence their decisions. They will have their depiction of their character, and if one is well-suited for war for example, you might choose it if you want to go to war. You might change them anytime, or during special sessions.
Technically, that would mean that, if we stick to the pantheons example, the citizens of different cities could have different ones. Generally, if you send a settler from one city that have a pantheon, they would begin the city with it, but they could change over (reasonnably short) time.
Example :
You start near two sources of game. The pantheon your citizens adopt is "goddess of the hunt", giving you +1 food and +1 production to camps. (although this example is pretty bad IMO, because worshipping such a goddess should give you less yields to this, not more, and there's no reason why worshipping that goddess would give you more yields in the first place compared to a camp without it) But, you started on a continent and is alone with no neighbour. You want to develop your navy. Next city you will settle would be coastal, and the citizens here will probably soon adopt "goddess of the sea", giving... well, giving bonuses to you ships let's say, like a particular promotion (because more food/production for yields can be trivial and the same problem than before, and that giving a boost to your naval production is not sensible enough) like "ability to raid coasts" or even better : "able to cross oceans". Then, if more cities are coastal and adopt this pantheon, say at least 2, you could choose this pantheon as official, and your capital would benefit from it too. There would still be other pantheons competition, and maybe if one becomes too strong there would a rebellion, but generally adopting offically one would give you enough "bonuses" towards it to be able to keep it.
