Everything on Earth supports its ecology - plants get eaten by herbivores, carnivores eat smaller animals, scavengers and small things like maggots clean up remains of dead animals, etc. Everything has a purpose.
But these cicadas only appear once every 13 or 17 years, live above ground for about two months or less while they mate, and then die off. The next generation burrows into the ground and remains there for another 17 years before the cycle repeats itself.
What is the ecological purpose? They serve as a great food source for birds, frogs, bats, etc., but this is only for two months. Most birds will never see a cicada during their lifetimes. If cicadas just disappeared, it seems like it would have absolutely no effect on the Earth's ecology, unlike just about any other animal or plant.