Take a solar panel on a little stand to a farm, at harvest time, and ask the farmer whether you can set your panel up in the middle of his field, and string wires back to the barn so you can charge a battery

That's a bit of a strawman argument-- the pitch of this type of setup is not to take all existing farms and plop down solar panels on top. Obviously that wouldn't work. It's talking about giving farmers an option where they can plan their land use strategically so that the panels can make sense with certain specific crops in pre-planned situations. 

The study's investigation of which crops could benefit from the shade has been done in tandem with farmers of the region (Arizona, where this study takes place, where the solar resources are most valuable to capture as well):

The farmers help the researchers decide on test crops as well. Every spring and fall they grow beans, tomatoes, and a couple of types of peppers. They grow high-value herbs and spices, showing the potential additional profits that can come from intentionally selecting crops that might not otherwise grow well in typical conditions, but that can now grow well in the shade of solar panels.

They also work with leafy greens like lettuces, chards, and kale, which seem to grow better in this system. Plants in high-light environments tend to have smaller leaves -- an adaptation for not capturing too much sunlight and overwhelming the photosynthesis system. Plants in low-light environments grow larger leaves to spread out the light-capturing chlorophyll that let plants change light to energy. The researchers are seeing that in their trials: basil plants produce larger leaves, kale leaves are longer and wider, and chard leaves are larger. This is key for these crops because farmers harvest the leafy parts of these plants.

The solar panels themselves also benefit from the co-location. In places where it is above 75 degrees Fahrenheit when sunny, solar panels begin under-performing because they become too hot. The evaporation of water from the crops creates localized cooling, which reduces heat stress on the panels overhead and boosts their performance. In short, it is a win-win-win at the food-water-energy nexus.

Having these farmers involved in desigining the study help bring to light any potential concerns:

When it comes time to harvest the crops, it is actually not a big hassle, explains Barron-Gafford, as farmers can use much of the same equipment. "We raised the panels so that they were about 3 meters (10 feet) off the ground on the low end so that typical tractors could access the site. This is was the first thing that farmers in the area said would have to be in place for them to consider any kind of adoption of an agrivoltaic system."