One big thing that has to change is peoples mindset on 4X. Expand, explore, exploit and exterminate is less than one half of the story of empires. Civ does a great job with 4X at the beginning then it falls apart in the middle because 4X is not a good representation of empires in the middle and latter stages of history. Civ muddles along trying to define what empires do in the middle and latter stages but it doesn't have a coherent model of that and so the game just falls apart.
The problem is that all Civ games assume that Human History has been continuous: that the aspirations and goals of Empires, States and Settlements/Cities 4000 BCE are the same in 2019 CE.
Therefore, there is no room in the basic game concepts for 'real' Dark Ages, replacing Science with Religion/Faith and then reversing that, changing the reasons you place Cities and grow them and why or even whether you make war and how you make it. Rules change, are accepted only partially, are enforced explicitly or implicitly, and Real World Historical Events change peoples' and empires' perceptions of what is necessary, desirable, or possible.
Virtually every population in Europe was Enthusiastic about going to war in 1914.
In 1939, even in heavily-propagandized Nazi Germany the population was nervous, scared, and not enthusiastic at all.
Today, a General War is almost universally viewed by populations and governments as an Unwinnable Proposition, even disregarding WMDs: "conventional" weapons can do quite enough damage, thank you.
And that change in attitude took place in less than 100 years: 1/60 of the game's time period.
Civ VI, at best and only sporadically hints at any of this.
Any body out there remember SMAC? The Factions had very different ways in which they would grow, and most of them spent most of the game building up "conventional" military forces based on technology and machines. Then, as you reached certain levels of Biological Technology and understanding of the native/Alien lifeforms, the best strategy was to convert to a military technology based on Bioweapons and Alien Technologies. That mirrors History here on earth: after 5500 years or so building up militaries based on muscle weapons like swords, lances, and bows, suddenly warfare became based on chemical power (gunpowder) and Mass Manufacturing (iron, steel, cannon, vehicles, tanks, aircraft, etc). The army that showed up on a battlefield in 1800 CE with pikes and swords would have been massacred. That same army by 1920 CE would have been massacred without ever even seeing their opponents.
Things Change.
It took about 5800 years after the Start of Game in 4000 BCE for there to be more than a half dozen cities in the world with 1,000,000 inhabitants or more. Today this post would have to be pages long to list the number of cities in the world with 1,000,000 people, and the number of cities with more than 10,000,000 is in double digits. As stated in the previous post, Growth has expanded exponentially, and the game doesn't reflect that - or the problems that growth brings for the people and their governments (and only skims the problems it brings to the Environment).
To incorporate all this into the game would result in a much, much more complex, subtle, and in many ways Non-Linear game: everything from 'best' strategies to Victory Conditions would have to radically change. For one thing, a Civilization based on some Bonus or Unique from one tiny period of history would be Unplayable. The basic design assumptions of the game, in many or most cases, would have to change.
Honestly, I'm not sure how such a game would be received. I'd like it, but I'm not a typical gamer (Typical Gamer = the Unicorn all game design teams are chasing) and I'm not sure such a beast inhabits these forums, so we may not be able to evaluate such a game from a marketing standpoint.
Assuming the design was done well, I can be absolutely certain that such a game would never degenerate into "same turn again" boredom . . .
The Civ 6 engine already has the coding to make cities start in a more advanced state when founded in later eras. When you choose Modern Era for your start, all cities you found are basically jump-started.
I think you could move that mechanic into the base game. A new medieval city starts bigger than an ancient era city, a new Industrial era city starts bigger still.
I agree with
@UWHabs, though, that the population growth mechanic itself does not age well. I'd like to see population growth be based on base population, limited by food, and then reduced or increased based on health factors. Then accessible food (whether from nearby farms or distant farms, self-produced or traded) simply becomes a cap on how big a city can grow, not the determinant of how fast it grows. Technology and investment in sewers, etc., dictate growth.
To address specifically the 'Growth Problem', the exponential Growth of cities in the last 200 years or so comes from three specific mechanisms:
1. The productivity of "Builders" IRL has grown enormously. First, with steel hand tools in the 19th century, and then Power Machinery in the 20th century, the ability of relatively small numbers of workers to throw up buildings, pave roads and streets, dig sewers and water systems and infrastructure, has increased massively from any previous period. For an immediate example, it took 100 years to built Notre Dame in Paris back in the late Medieval Era. They are planning as I write to completely rebuild it in 5 years. The Pentagon, a vastly larger if less decorative structure, went up in less than 3 years. A city started in the 20th century from Raw Earth will be larger than almost any Ancient or Classical City in a fraction of the turns (even allowing for the 20 or 40:1 ratio of years to Turns) they took.
2. Food Supply for a city/settlement for most of Human History was what was available within walking or cart-hauling distance: a maximum of about 100 km or so over a decent, or at least level, road. Or by sea of river from much further off. Once railroads were laid between cities and regions and powered (steam, diesel, etc) ships were built, Food Supply became Whatever There Is In The World and the City/Settlement can pay for. In game terms, City Radius disappears as a limiting element and Trade Routes become The Factor for city growth.
3. Population Growth in a city has never been dependent on people born in the city. Cities for most of history were very unhealthy places in which to try to grow a child (Rome averaged an epidemic of some kind every 15 - 20 years in the 4th and 5th centuries CE), but people were constantly moving into the city from the countryside to get near the Jobs, political power, and amenities (IF you wanted a Circus, you had to go to the Circus, it wasn't coming to you until P. T. Barnum and his contemporaries much, much later). So, when Mass Media (starting with regular mass newspapers in the 18th century) and Fast transport (railroads, steamships again) became available, Internal and External Migration became almost unlimited for City Growth. the growth of New York City, London, Paris, even Moscow in the 19th century would have been simply impossible 200 years earlier: the food supply, migration, and viable living conditions for such masses were simply not available. Shanghai and the other Chinese 'Mega-Cities' (or Mexico City and other examples) in the 21st century did not have 10,000,000 + people get born in them: their inhabitants moved there from rural villages - the migration into cities has, if anything, gotten more rapid and massive in the past 50 years throughout most of the world.
So, and this goes back to the Non-Linear nature of the Real Human History, such a basic thing as growing your cities in the game has to undergo a complete change of factors and conditions and mechanisms in the late game - and the problems and decision-making that the gamer/AI has to tackle for city growth must/should also change.
