This is a great idea. We have had similar problems. Either some group members would not get involved in the storyboard process once it got complex, or in creating a storyboard for a video (which ended up as our “product”), we ended up with too many cooks and finally gave the task to an experienced copywriter who was a member of the team.
Your tweak would at least keep the team more involved and while you might still want to assign a single person to write the story, they would be doing it with far better input. Thanks!!