They break down quickly
Natural pesticides like rotenone and pyrethrin break down rapidly. That's why they have to be applied frequently. Makes them safer as well, since they don't have long-term toxicity. Good organic farmers use a variety of pest control strategies other than spraying pesticides, such as interplanting different crops to confuse or repel pests, creating conditions that encourage predators, or releasing predators.
I suspect the study you link to was funded by agribusiness interests.