What are the ecological consequences to "Palmetto Bug" extinction?

I live on an island in South Carolina and face these giant cockroaches daily. I am not an insecticide fan, but, after dealing with them for years, I am sorely tempted to spray the heck out ouf the little “buggers”. Do they serve any useful purpose and is there any reason (beyond respect for all living creatures, etc.) to spare these odious beasts?

They will be the only ones left to keep you company after a nuclear attack … be careful or they could turn on you!