They're farmers, but they aren't farming based on a sustainable model.
Nothing will end pest problems, but appropriate design will mitigate their impact on a system.
Chemical pesticides are less than 100 years old. We got along just fine for beforehand for millennia without them.
Here's another interesting fact - every culture that has adopted "modern" agriculture (i.e. the practice of clear-cutting forest, tilling soil and living primarily on annual (largely mono) crops) have eventually collapsed. All of them. It isn't a long-term sustainable model. Look to the lands of the middle east that were once lush edens for a prime example of how desertification is the end result. Look at the dust bowls of mid-western america as an example of how industrialization has only accelerated this process. Topsoil is the largest export of North America. The midwest prairies once had 6 feet or more of topsoil, until the clearing and tilling began. Contrast the long-term sustainable farming methods of North and South America (i.e. thousands of years), where the ratio of forested to cleared land for cultivating crops and grazing cattle was far different before western culture to what exists today.
The "simple" solutions do work (they aren't simple in any way, however, as it is the complexity of the natural system models and patterns that make them work). Every long-term sustainable culture has relied on them without fail. And I don't buy the usual retort of "try and feed the world with them". There are plenty of documented examples of permanent, sustainable agriculture (i.e. permaculture) systems that provide as much abundance and nutrition per acre. It's just a matter of appropriate system design.
I'll trot out the usual permaculture examples of proven systems and people leading by example:
Sepp Holzer and his Krameterhoff and Holzerhoff farms in Austria
Masanobu Fukuoka, who's system in Japan was rated the top 5% of rice production per acre in the country, yet also yielded an annual crop of barley on the same plot - all using natural methods.
Bill Mollison and the permaculture research institute in Tagari, Tasmania, and the PRI's he and Geoff Lawton have set up world wide, many in some of the most challenging environments in the world (i.e. the salted deserts of Australia and Jordan)
Mark Shepard and his New Forest Farm based in Wisconsin
The large-scale grazing practices based on Alan Savory's work to reverse desertification
etc