Cockroaches do play an extremely important role in nature, as they are sources of food to other organisms that we humans eat.
Their a valid source of the food chain, which some certain members can't live without. The parasitic wasps for example are solely dependent on cockroach eggs as that's their source of food.

Cockroach are also source of medicine. Due to their innate ability to regrow lost limbs, scientist are finding medicines to regrow tissues from them.

Actually I which we could exterminate all cockroaches but I've deemed that thought highly impossible and selfish 😭