Check the "Lunar test" savegame I have in my folders. The cities there are only 2 tiles away from each other. While it matters early to a certain degree, in the renaissance a point is reached were cities are purely beneficial without anything then a traderoute connection. Also there are so many +

and

buildings by then, that they basically don't need to work a single tile. So the "more cities to win" strategy is totally valid then.
2 tiles away, or 2 tiles between? C2C has a limit of 2 plots between cities so unless you have changed it that should be the limit.
Thunderbrd's rambling is correct too, having more plots to get either hammers or commerce or food can make that city produce faster, spit out more science (but not gold), or grow bigger (but not faster).
But this is a truth in moderation.
True, one city can have a very high production and build Wonders faster. Also true is that you can not have more than x Wonders anyway unless using specific option of no limits. 2 cities can build more wonders together because of this even with less production.
The same goes for units, though with bonus XP one can have more XP with one city you can have 2 units from 2 cities, which in many cases countrs for more than some bonus XP.
Science from a science output city, or from 2 unspecialized cities?
And so on and on.
The one thing that I can consider is the one thing you did not mention Thunder. *grin* Maintenance.
Little space between means more cities needed for the same effect in the end, so more in #Cities maintenance and in total costing more gold for the same output.
You do gain a bit in DistanceMaintenance costs though, and a little in not having quite as big cities in the end game too.
What we all are about though is when limited space exists more cities can give a bonus in the end. This is also part of the reason why I some times advocate for reduced science for more cities because it is the science that determines the better strat with more cites, regardless if they are spread out or nestled close.
Peoples examples of AI being ahead in tech and thus spitting out 4x the cities the human has makes for a hard game where the human will always strike from behind, even counting help from Tech Diffusion as that is based on your tech output and not how far ahead the opponents are.
Cheers