And if you step out all the parallelism from your concurrency runtime, you get rid of a big chunk of the overhead. But even with purely cooperative single-threaded multitasking, there's still some overhead vs "ordinary" strictly serial code.
I have seen egregious abuse of pre-emptive threads ... a lot. Abuse of green threads / fibres / coroutines ... not so much. I think one has to be a half decent programmer to be even aware those options.
This isn't a hard and fast rule. There is overhead to parallelism.