Just having bigger maps isn't the best solution for late game overcrowding and unit micromanagement because it would affect so many other aspects of gameplay. How close are civs going to be to each other? How closely spaced can cities be? What about resource density? How fast can units move relative to the new map size?
A much better solution would be to move tactical combat to a separate map, so they can go back to stacking units for strategic movement and retain 1UPT for combat. And the days of "route to cancelled" would be over as well
I think those problems would auto-solve just as they are in Civ5 with different map sizes, not even considering the possibility to add more civs on the map hence modifying the proximity to each others.
Now, it's true that one can disagree with the defaults. For example, I always wished I can find more types of different kinds of resource near my starting point. (it would be win-win : more resources makes for more happiness, but i have to connect them which require an effort and competition from other civs) I think this cannot be modififed in Civ5, even if you increase dramatically the number of civs.
Also, people can want bigger maps for other considerations than mere logistic. For example, to have a better sense of the gigantism of the world. For things being more immersive and epic. What I have to say about Civ5, is that it dramatically lacks of epicness according to me. First thing, everything seems worldwide very early. (denouncing... so UNO) There's no this feeling you are a part of a small culture among others in savage times, for example. Even the style of the interface shouts it.
There's also a problem with exploring / rights of passage. Either you shouldn't know the world so early, either some remaining blanks are not realistic gameplay speaking. So either exploring shouldn't have such a range, either the absence of rights of passage shouldn't prevent you from exploring. All depends on what we want to represent with exploring in Civ. Most of the time most people just knew their direct environment. But, people migrate mostly by need (which implies "free lands" in some circumstances at least -people by themselves, and even cities, occupy an insignificant portion of the land). People trade. People talk, they can hear rumors. So what is exploring ? Is it having a precise notion of geography or just the ability to enter in contact or simply having some knowledge ? It's crucial for determining what type of feeling we could have in a Civ game, and as to consider it more like a board game or like a grand History immersion.
As to city density, it's all related to ICS. Do we want to settle cities regardless of space and resources, or should we make it so that we take attention to them when settling ? I would say it is of no importance if we want to fully settle the map as i want. Because, instead of settling cities right next to each others, you will settle them right spaced of each others. You will simply increase the space there is between them, not considering or not if you plant a new city or not. There will just be cities better than others, but nobody can ever avoid it. The "avoiding ICS at all costs" philosophy brang to Civ5, with full spaces full of nothing, which is a complete aberration history wise.
I suggest instead than we settle a new system of cities. For example, ICS should be natural at first. I would even say : for each tile, you may have a city / village / settlement. Later on, some cities can take more importance than the surrounding villages / settlements. At last, we have the rural exodus. (industrial revolution)