When I was growing up in fly-over land, we had small, harmless little ladybug beetles. The most benign of all the flying insects in the territory. Then some how an aphid that attacks soy bean plants got imported from Asia, no one knows how for certain. It attacks the stems of the plants and destroys their ability to transport moisture through the stem. Pretty devastating to the plant.

So Very Wise People imported an Asian ladybug to feed on the aphids. Very large in comparison to the native species. And they bite. And they leave dirt trails when they come into the house. They have helped mitigate the aphid problem, but the native species is pretty much gone now. And the Asian ladybugs move into your house for the winter and invade everywhere and leave their dirt everywhere. And bite.

So, net result: One destructive, invasive species somewhat tamped down, but farmers still spray insecticides for it when it gets out of hand (based on population measurements in growing bean fields). One native species wiped from the ecosystem and replaced with a nastier and more populous non-native species. Net it all out: 2 for the invaders, 0 for the home team.

There aren't really any simplistic answers. Chemicals aren't great for the non-target species (including the farmers that apply them), but imported predators have unanticipated side-effects as well. Not growing soybeans anymore is an option, I suppose, but not so great either.