Add a way to quickly assign a task to all individuals in a user group.
See the "assign to group" in this mockup. This would be a subtle link, to avoid people haphazardly choosing the group by mistake.
Also, it could bring up a confirmation prompt, similar to when you assign to an external user.
Point of distinction - This is NOT assigning it to the group itself. It's just a shorthand way to add the individuals with less clicks.
I think this would make many people happy, without requiring a logic change.