Then you can get into what you mean by FP - if you share nothing then your communication is done by copying. This is not a magic bullet and isn't an option for many scenarios. If you do shared state for join parallelism you can cover other scenarios, but now you are sharing data.
Atomics are very fast and work very well when they line up with the problem at hand. Then again, you are creating some sort of data structure that is made to have its state shared.
If the problem was so easy to solve, it wouldn't be nearly as much a problem. Handwaving with 'just use FP' is naive and is more of a way for people to feel that they have the answer should anyone ask the question, but reality will quickly catch up.