Whilst I agree in part, in my opinion it's the centre that makes the key call.
It is them who must decide if the short ball will find the crash man and they'll need to help the half, or rather to push of and drift with the FB to make sure the winger isn't left stranded.
It's them being the main decision-maker that makes it the most difficult position.
In my opinion of course.
That being said, if the second-rower is slow laterally, they can really expose the half and make his job infinitely harder. Ice was a perfect example of this last year. He was TERRIBLE at over-committing, bringing that key decision one man in to the half as you said.