This a topic I´ve been wanting to open for a long time, but didn´t have the patience. SInce it´s here... Those are very good ideas and a good change from the formula we´ve been getting. I confess I am not very fond of the direction the game has been going, losing many mechanics that used to give the game more depth in favor of ones that for me, fell more gamey and only there to give the player one more thing to do. On my part, the biggest change I like to see is a change in focus from the city based model to a pop based one, where the PoP has the abbility to work the land or the improvement in the hex or move to the city.
The city would be like a special improvement where the magic of "civilization" would happen. So I would have a separation between cities and country side. In the country raw materials are collected and some processed and in the cities is where commerce and industry and religion happens. Not only that, but I would have pops breeding independently, based on resources and other factors and spreading through the map and my job would to keep them satisfied and occupied and inside my culture instead of going their own way.
I would also create a separate screens for the cities and internalize districts and wonders. I would base the city in the city center, that would hold some buildings and have a hex based map around it. the city would grow based on the districts I´d build around it. The buildings could provide housing or I could build housing as a building and that would be necessary for the citizens inside the city. The distance from housing would affect productivity. That would create a nice dinamic between getting bonus from productive buildings and the necessity to house everyone or risk slums. This model would provoke a push towards expansion, a reason for colonization, internal upheaval and many dinamics that can really spice the role game.
The City has always been the focus of Civilization games for just the reasons you mention. The separation between city and Elsewhere was traditionally the City Wall, which is found in the earliest settlements/cities dating back to 9500 BCE.
I have an entire separate document in which I'm gathering my thoughts on organization of a City in the game, because I think putting as much as possible on the maps in Districts in Civ VI was a brilliant move, but not implemented well enough.
In brief, I would increase the number of Building slots in a District tile to 5, make any adjacency bonuses apply to the Buildings in a District instead of the Districts themselves. All Districts could be Themed for more bonuses, none would be inherently Commercial, Religious, Scientific, etc. If the majority of Slots in a District were all occupied by buildings from the same area of emphasis, then the entire District gives a Theming or Adjacency Bonus to those.
Housing would be included in most of the early buildings, since in most of the world people lived in back of their shops, workshops, places of business. Only with the Industrial Era would Production Buildings like Factories (which would take up more than one slot, representing their Size compared to earlier Workshops) start to become completely separate from Residences, and at that point adjacency Bonuses from having Residential Buildings near the Factories would come into play.
The one exceptional District would be the first one, the City Center, which would require an Administrative Building - Palace for the Capital, Governor, Prince, Mayoral structure of some kind for other cities. Other Buildings in the City Center would depend on your emphasis for the city and sometimes the Civic, Governmental, and Social structure of your Civ. For example, a Theocracy government would require that a Temple be constructed next to the Palace, while a Constitutional Monarchy or Republic or Democracy would require a Parliament or Congressional Building next to or near the Palace.
All Districts in a city would have to be adjacent to each other: separate Districts would be Settlements and represent individual smaller towns feeding Resources or Goods to the city. Each of these would have to have some kind of Resource structure in one or more of their building slots, like a Grange or Grain Elevator to store and ship Food to the city, a Refinery, Smelter or Forge to ship Production, etc.
Distances from the City Center to the rest of the city, and from the city to Resources, would vary tremendously during the game. At the start, you could only build out one ring of Districts (with some exceptions). As transportation gets better, with better roads, vehicles, horses, the city could expand. Get Steam Transportation as in railroads, street railways, and later the personal automobile, and effectively there would be no restriction on the distance from which Resources could be supplied to the city, or the distance to which the city could expand. The late Industrial and post-Industrial Era of powered transport should see in the game the same massive expansion into Megalopolises that occured in the late 20th century, with Urban Conglomerates extending hundreds of miles.
Ideally, planning and administering to a late game City should be an entirely more complex undertaking than keeping an early city going, and most of the buildings and structures in the late-game Metropolis would be very different in size and efficiency from those cnstructed around the City Center in the early game.