If the insects are fed naturally, it would probably be more cost effective to feed the chickens whatever you are feeding the insects. The only reason to introduce the insects would be if you were using something the chicken cannot eat, like wood.
Same with humans. It's much more efficient to feed humans directly than animals for human consumption.
Living organisms don't metabolise and transform matter in the same way.
A chicken eating an insect who ate a plant could produce higher quality feed and thus chicken than if the chicken ate the plant directly.