CPU can do billions of operations every second. When you have 200ms for every request that overhead is not that large, you're still blocked by I/O.
I built a service that was making a lot of requests. Much enough that at some point we've run out of 65k connections limit for basic Linux polling (we needed to switch to kpoll). Some time after that we've ran out of other resources and switching from threads to threads+greenlets really solved our problem.