With effective unlimited resources, gigantic farms become possible, and with future tech, can likely be automated on a very large scale. Possibly with the only human intervention needed being an overseeing one, looking out for things needing maintenance or adjustments.
Why would we use Hydroponics instead then? Because if we are going to be fully gene editing plants anyway, just splice them on some kind of aquatic plant, and have them grow underwater. There are a few reasons why you could choose it over land based farming.
These example reasons are for plants grown on a long artificial (outdoor) hydroponics river:
Easier to maintain a steady temperature.
Water has a good heat capacity. It can store a lot of heat, and is easier to maintain at a steady temperature than the air would be around ground based crops at these very large scales. It would kind of 'insulate' the crops from the air. The insulation would ensure that extreme shifts in temperature and weather crop failure would be lessened.
If we place the 'growing river' near large buildings we can use the river as heat-sink and thermal mass for them. If we place a shallow roof-pond on top of the building (covering most of the roof) we can use it for passive cooling during summer, and heat transfer from building, to the crop river, simply by making the water flow towards the river, along a sloped side, using gravity. During winter, it would recapture heat from the building, ensuring that there is less heat wasted, and the system also functions as a rain gutter for gray water.
We could also use geothermic heating for the crop river.
Easier to maintain nutrient cycles.
Soil depletion is a thing. If we remove soil from the equation, we can't have it deplete. Jokes aside, keeping a constant level of the needed minerals in water is again easier than having it need to be added to the soil every year orso. We can simply directly add the nutrients to the water, and they will mostly spread themselves. If we go with slow-steadily flowing water, we can get away with adding nutrients upstream, and measure nutrient values downstream.
Giant fruit/vegetables
One of the best things about growing underwater would be that plants won't collapse under their own weight. As long as the buoyancy of the fruits/vegetables is near that of the water, the pull down/up on the rest of the plant won't be much. This means that a plant can get away with a lot bigger fruit, without needing to grow on the ground, taking up extra horizontal space, or needing sturdy branches.
Steady Produce
Because of the controlled temperature year round, and enough sunlight, we can also grow things in batches. Saving both storage space, and allowing for fresher produce year 'round. I imagine the plants being grown attached to floating baskets, which slowly drift downriver. Batches could be separated by some floating separation rope. Separate them by a week, and you can have many batches of produce in different stages of growth on the river. Creating a new ripe batch each week.
If you make the river O or U form, you can easily move the water from the lowest point back to the highest one. Doing so ensure that produce collecting and (re)planting could be done in the same location. The river could be a -longer curving back and forth snake shape- for produce that take more time, or a very large O so that many buildings can use the river as heat-sink, and a city wide dump for grey water. (with an overflow somewhere).
Could we use aquaponics instead of hydroponics?
We can take the used water from the hydroponics, and feed it into a few small ponds. Fish would produce 'food' for the plants. The plants would then ensure the water was clean again for the fish. Some filters might be necessary.
I imagine the ponds as a side channel to an large O loop, keeping the fish separate, but having a part of the water flow from-, and back to-, the artificial river. The ponds could serve multiple functions such as a nice pond in a park. Even if the people don't eat the fish, watching them might still be a enjoyable pastime. Filters can ensure that fish and food are kept apart.
These ponds can also nicely work to store water overflow caused by periods of rain, as to refill our river during more dry periods.