The FBI used to and still may favor #4 buck, Shawn, for the reasons you cite.
The HD 870 here at Casa McC has two #6 field loads up first, followed by 00. The premise, if I need more than a shot or two, I might WANT to shoot through the fridge or something.
When it's not deer season, the deer 870 gets a IC or Modified tube instead of the rifled one, and is topped off with 00 for backup.