Mostly it's for two reasons 1) production and 2) space. With all of the other linear inputs in the game, there's either other ways to get them or you get very little added beyond 4 or so initial cities.
You get more Production right away. The city tile itself gives a few, then you also get to work another tile for free. Not only in more raw hammers, but you can also split among different projects, building an archer in the other city while continuing to build a Wonder in the Capital, for example. This has great practical benefits, even if they're not as measurable in hammers per turn per civ.
Space is the other key thing, whether for strategic, economic or religion reasons. Strategically, it's easier to defend the 4 or 5 cities of your empire that really matter when the AI is off taking some outpost on a second Continent, or stuck on your borders taking fire from your Archers. It's also easier offensively to have a point of retreat and a place to heal that's closer to your objective. Also economically, sometimes there's just a plot of land that you want to hold rather than surrender to the AI. You wouldn't want to give up a prime food locale to an AI, because that city will grow super fast, and then the AI might produce Settlers there and come in for even more. Giving up marginal terrain would be ok though. And for religion, it's increasingly easier to keep and spread a religion for each city you add. You might care very little about the follower benefits in that city, but the Pressure keeps your core cities safe, and helps your own spread too.
Another thing is just raw Faith. Without a powerful faith generating Pantheon like Desert Folklore, you've basically got Shrines and Temples and that's it. There's no Faith specialist or higher tier Faith buildings that you can build. So, the only way to do it is more cities.
Other linear inputs are not helped as much.
With Gold, players will just puppet captured cities and spam them with TP's. Also in general, gold earned by tile yield in 5-6 pop cities is quite low unless you focus on it somehow AND you manage to have a good deal of the multipliers like Markets and Banks. Meaning that for the relevant portion of the game, most of your gold output is going to come from your 4 core cities, particularly river tiles and luxes there, then some from trade routes, some from trading luxes, and some from added puppets/cities. As as for trade routes, the formula for yield actually looks at the size of your capital, if I'm not mistaken, such that there is little benefit to adding an additional city after a certain point. Then again, there is always some marginal benefit.
Same with Science. You get one National College, and only a few Academies during the course of the game. Universities are helpful, but it is hard to build them in your 10th city at a decent time for a Science win. If you do have enough money for multiple Maritime allies and to rush buy Universities in new cities, you are probably about to win anyway. Before then, it's hard to staff the 2 scientists in a 6 pop city before you hit Freedom. Which is why wide-Science isn't really a big thing. I've seen some Korea games with 8 or so cities, but that's as wide as it gets.
And then obviously, Culture is directly curtailed, and there's the diplo concerns of trying to overrun the map.