[dejv]

Not only FAA, there are additional regulations that prohibit use of aerial vehicles to spray crops. The reason to do that is to minimise chemical pollution to other fields/nature. These regulations depend on country and few other things.

[frisco]

Crop dusting is very common in many countries: https://en.wikipedia.org/wiki/Aerial_application

[jqm]

Yes, including the US. Spraying crops with airplanes is very common. Not sure where the idea it is banned comes from?

[dejv]

Yes, they are very common in countries where the short term profits are king. The problem with aerial spraying is wind: you don't want your herbicides/insecticides to be sprayed out of your field: as it can kill bees or local population of butterflies and other insects as well as local herbs and plants that grow around.

In EU we banned the aerial spraying (in most cases) as well as have quite complex rules to minimise this pollution: like not using spray in form of aerosols and such.