Insect populations react to their food supply, hey don’t predict it. Even if you found a way to make a pesticide that only killed the herbivores, the predators would starve without other food sources. Many predator species including ladybugs, lacewings, and predatory wasps feed on and/or shelter under umbel flowers. Especially in their adult form. Ladybugs don’t actually eat many aphids. They leave that to their children.

So you kill every insect, and then the pest species come back in numbers before their natural enemies even get their pants on.

This presents less of a problem if you can borrow them from nearby healthy ecosystems, where the pests are under control. See that long enough and you start to wonder if you can just put away the pesticides and grow different plants instead.