It's a happiness issue but it's also a food issue. Vp has added so many components that produce food and citizens still eat the same amount of food than in vanilla so improvements like farms are useless. If you just look at how many buildings from the ancient and classical era produce food in some way you get what I mean. It all adds up and growth outpaces happiness.Like all things it depends. In my capital, and perhaps later on in a few select cities, I can not get enough food. Food isn't in that regard the problem. The happiness system is the problem. That is why you lock pop growth in your later founding cities. They have to much food and can't handle the unhappiness, mileage may vary depending on game difficulty and such. So I do send trade routes with food to my capital if I can. Bulking up my capital is more important then getting some poultry little gold and culture reward from a foreign trade route, that also have a lot more risk involved. I don't tend to lose internal trade route, the same can't be said for the non-internal once -- city-states or foreign lands matter little in that regard as they are both horrid at barbarian control and war declarations -- intentional once or those that they get dragged into.
Is sending trade routes with food creating food out of thin air? In some regard yes but on a conceptual level I am sure it can be explained. As with all things in the game a food produced might not be food eaten. Most people don't go out into the field and eat grain straight from the ground. You do something with it. Processing. Just like you don't go out and just make things out of trees or stone, they are processed for production. We just don't really see the processing in the game, Some buildings and such do give a little bit of food or extra food on resources. I guess those could be considered the processing of food. Otherwise a lot of it is tied to pop growth, as in spill over when a new pop is born.
But over all I would stay this is not a food issue, it's a happiness issue. It takes some time for you to get all the happiness things online in small cities. But this is what you get I guess when it distributes things over all cities. Getting a new city in that regard sucks a bit. Even if you build it with a improved settler such as a colonist etc the basic buildings does help but not enough. The people in those cities will almost instantly require buildings that grant happiness that are out of their reach in some regard.
I guess the main thing I would agree with is that farms are horrible improvements. I rarely build them until late in the game. The yield isn't really needed for growth as much. The second reason is that horrible event that just keeps happening over and over and over again where there is flooding. If you don't build any farms you never get that event triggering. So it's just not worth building them if you constantly need to send workers there to repair things and hope that the flooding doesn't destroy other things. Worst event ever.