I actually love this idea and/or the general idea of changing the way land is handled in the game. If a city occupies an entire tile, would the subtiles host different buildings? Would the city's growth slowly envelop more of the subtiles on its tile? How would improvements work with subtiles, could you do something like build a fort on a perfect defensive location subtile without losing the ability to build a farm if the tile was also good for that?
First of all, I have to say that I didn't think about all the details that needs to be worked out. This would also depend on the developers how they want to implement such a feature. But I will try to give an example how it could be worked out depending on your questions. Cities could start on only 1 subtile and slowly grow to other subtiles of the city tile with population, era advancement or certain buildings.
(Possibly it could be done that each subtile, except in the center, could have a distinct specialization think of districts in Rise of Legends if you know the game. But this is maybe to detailed and complex for an initial concept thinking.)
Conquest of a city is then also of importance. Does the whole of tile in which the city is placed as 1 part, or do each subtiles have to be conquered separately? When is a city considered captured, if all subtiles of the city is taken or just if the center/initial subtile is taken? And if a city is captured partly can it produce buildings/units? You could think of city combat as in modern combat in cities. Here many things that is involved to this, but this would be a bit dependent how well the AI could handle these changes. If it would be a too drastic change then it could be that all the subtiles that belongs to the city is considered 1 whole and an attack to a subtile part of the city is directed to the whole. This last option seems more appropriate considering the current AI.
Regarding improvements and worker actions. My main idea was that each subtile would have its own improvement on it. But this introduces a new problem. To improve each subtile one needs to do a lot of micromanagement with workers, which I think most players would not desire. To improve subtiles a different type of worker actions could be introduced without worker units. This could also be benificial to the AI too, because then the worker stealing would stop. One option is to function it as in Call to Power 2: by placing on each tile the improvement with a mouse click and is finished after certain number of turns. This is only one possibility for working improvements and worker actions out. Again the best choice would be made as such that the AI could handle it and it is not to much of micromanagement for the player.
However these kinds of questions worry me with the design. It seems like it would make movement, improvement, and city placement/content too complicated. If it was made to be specifically for combat I think it would be nice, but then you'd have to change the way cities and improvements interacted with combat. Not that it couldn't be done, it just seems very complex and somewhat hard to balance/work out.
I suppose you are reffering to movement, improvements and city placement for the player. Yes, this could be a pain to the eye if it is not worked out properly in the user interface. But, I can imagine that it can work out well if the user interface would highlight the movement possibilities of a unit, the city placement and its possible cultural borders. City working tiles could be reduced back from 36 to 18 (from 3 tile distance to 2) if needed. For the improvements I already indicated above. All these graphical additions would definitly require a much better gpu too, I am not sure if that is possible to handle though.
If you are referring to difficulties for the AI, then I would disagree. I consider it would better for the AI moving its units around. For city placement it wouldn't be any different as it is now. But for improvements with workers, could be a problem. Because as I understand players think that the AI is not using its workers efficient and with more subtiles to improve this would be more of a problem.
One of main purpose of this is to change the combat such that more space is available for unit placement (7 times the current amount) while having the number of units either the same or increase it just slightly. But this could be done in combination with other possibilities it would offer.
Regarding balancing. It would be better to indicate in which aspect you see issues with balancing. If you are referring to tile yields, I don't think it would be a problem at all. As most of the tiles would consist of mixed subtiles this would easier to balance, because the subtiles with superyields or useless ones could be averaged out more easily. I don't think that combat on subtiles introduces new balancing issues. The movement points on the other hand should be changed accordingly, but I don't expect that it would introduce new issues.
Well it would make it more complex for gameplay. But wasn't that one of the things what players were complaining about with Civ V, that it was made more simpler? I think that a new Civ with well worked-out subtiles has many new possibilities and fun gameplay. But if it isn't worked out well with user interface and AI, then it would turn into a disaster.