I understand the concept of population growth being linked to faction prestiege. People are attracted to the most glorious factions, and good living conditions, national pride and identity all serve to enourage population growth. What seems a bit awkward, at least in terms of story, is why is faction prestiege affected so little by what a faction actually does?
IMO, prestiege should be a measure of how good you are at whatever it is you have chosen to do. Does you sovereign perform epic quests? That should increase your prestiege. Do you research techs that no one else has discovered before? That should distinguish your faction. Do you build unique buildings, control unique locations on the map, conquer powerful enemies, field massive armies, conquer wildlands? These should attract people to your cause. Conversely, a faction that sits in the corner of the map and does nothing is unremarkable and unattractive. Someone who loses important battles, has their heroes routed and accomplishes very little should not be prestigious.
Perhaps faction prestiege should be viewed as more of a resource that can be gained, lost, earned, traded by various means. If you want a kingdom that will grow massive cities, then focus on accumulating that resource and bolster your growth. If your kingdom is far behind in prestiege, then it should have consequences, like reduced growth, unrest, reduced area of influence, diplomatic effect, having troops abondon your cause, or loss of population to your more prestigious neighbours. Balance the power scale by factoring in both prestiege and raw military power.
Maybe what I am talking about here is a merging of faction prestiege and influence/diplo-cap. Give everyone a base amount to start the game, and then base the effects on the global "prestiege market". Trading away influence to another faction means trading away growth. Provide various ways of gaining or losing it, like doing (or failing) quests, special buildings, spells, payment for diplomatic actions like ending/starting wars, X influence per turn that I am the only one with a given tech, pay a tribute of prestiege (like a vassalage). But most importantly, have it mean something that you have a lot or little of it.
Diluting your prestiege is supposed to be a negative motivator against city spamming, but the way it is implemented by splitting it by city first, then calculating growth doesn't make much sense in terms of immersion and storytelling. If your global influence just attracted X people to your faction per turn, and those people were then distributed amongst your cities with food, it would still have the effect of growing fewer cities faster than many, and it would eliminate one issue we now have. Currently, if your city has no extra food, then the influence allotted to that city is negated and has no effect. If your total faction population growth were based on your relative influence and divided amongst your cities that have extra food, then your influence has full effect and is not wasted. If you have no food available, then your faction needs to expand to find more food sources, either by buildings or by expansion, or it will lose the benefit of its prestiege. This method also allows the possibility of regulating global population growth as a means of controling pacing. More population per turn = faster game.
Simpler is usually better and I am not really getting why there is both faction prestiege and influence. Why not combine them and then amplify their impact on the game. It would certainly spice up the political aspects of the game.