To the original poster: whether or not the majority of your research comes from population or districts/buildings is only somewhat relevant (it's tangential) to your original question, why players settle their cities so closely. The key is here:
The reason wide is so much better then tall in VI is because of housing and district limits.
Housing is the chief limiting factor and the total number of districts is the advantage that you want to leverage:
-Housing limits your maximum population far earlier than number of available tiles. Fresh water plus an inexpensive granary gets a city's housing limit to 5, which means it can quickly grow to only size 3, grow slowly to size 4, and crawl to size 5 or 6. You can increase this limit of 5 a few points with some tile improvements, possibly some cards or government choices, and maybe another couple of points with district buildings, but those are only available in what many consider (please don't derail in disagreement) lower priority districts. You also get diminished returns on rainforest/marsh chopping and food resource harvesting when your city is near its housing cap. SO, you're going to run out of housing far earlier than you'll run out of tiles, even with cities only 4 tiles apart. Now, this situation radically changes when neighborhoods become available, every city can have nearly unlimited housing. But neighborhoods come quite late in the game, arguably after the conclusion of the game is already determined, and what happens during the turns before neighborhoods become available is considerably more influential on a game than what happens after. (side note: this is something that makes the Kongo civilization at least interesting if not powerful, because they can side-step the housing limitations much, much earlier than other civs)
-total number of districts means power (at least in all but the highest difficulties. There, hammer efficiency is so cut-throat that many consider a district-less empire the best way to go at deity, but back to conventional strategy....) There are many reasons for this, but just a quick, non-comprehensive synopsis:
1.) district/building yields are essentially free. While a mine's four hammers are more than a workshop's two hammers, the mine requires that you allocate one of your citizens to work that tile while the workshop is a passive two hammer bonus added to every turn. 2.) adjacency bonuses can increase those passive yields 3.) most of those passive yields that you're getting, from the district or the adjacency or both, can be multiplied with cards. 4.)city-state type bonuses for 3/6 level envoy - this can be huge. 5.) great people - also huge.
So having a great number of districts can allow you to do more things. That being said, there are two (more) advantages to a wide empire vs. a tall empire in this context. First, one city can only build one of each specialty district, a size 40 city can only have 1 campus and 1 of each building, but ten size 4 cities can have 10 campii and a total of ten of each buildings. Second, it is very easy to manage the housing and happiness limitations of ten size-4 cities, and it is also very easy to acquire and build up ten size-4 cities. It is nearly impossible to meet the housing and happiness demands of one size-40 city and would take forever to get it to that status. It's for these reasons that wider is simply much more attainable, practical, manageable, and effective. So placing cities very close to each other helps in utilizing this.