In this case, one reason to look for psychological techniques rather than buying a can of insecticide is because of the child's goals. She wants to overcome her fear/disgust reaction to roaches. Psychological techniques have an excellent chance of accomplishing this. If she wanted to kill roaches, a can of bug spray would be a much better investment.

Also, the problem isn't an infestation of roaches, it's her overreaction when she does encounter a roach or when she anticipates encountering one. Bug spray is good for the former problem but not the latter one.