Take them away, especially mosquitoes and we're dead. The old food chain...
They kill us with the diseases they incidentally carry, but other than that, we're just their cows and pigs, at least for mosquitoes and ticks. Roaches are great recyclers, and likely don't care if we exist or not, though some species love human houses.
Looking for a purpose seems futile. They are just as random as we are, and good at what they do. We're kind of like roaches, when you think of it. Those parcourt people even run up walls, and a lot of teenagers stay up all night and shun the morning light. Sometimes they even seem to reproduce pretty quickly too!