There are a number of folks round here that also do the "staggered" pattern riding - usually the Harley riders that at least wear helmets.
While it is definitely more safe than true side-by-side riding, they are often still waaaaay to close together to be able to react and avoid road hazards in the lane or by the shoulder without risking bumping or crossing the yellow line into oncoming traffic. Just a couple miles down the road from my house we had an 80-something year old who shouldn't have been driving, drift his Crown Vic across the yellow line into the front of a pack of these riders who were in staggered, but too-close formation. He took out 6 bikes - killed a rider and his passenger and sent those on the other 5 bikes to the hospital. Those that he didn't hit directly got taken out by the "billiard ball effect" of bikes and riders or were forced off the side of the road into a steep embankment. If they hadn't been in such a crowded formation, there would have been less carnage. If they were in single file formation with proper following distance, I think that most, or all of them might possibly have been able to avoid the unguided octogenarian missile.
I always ride single file - or will ride in stagger formation wheel tracks within the lane but keep the similar following distance as if we were single file. But, I refuse to ride in close formation as it greatly reduces your ability to avoid collisions.