Whatever may have been done for government purposes, barrels were also moved to deliberately adjust their aging characteristics and when labor was cheap it wasn't such a big deal to move barrels around. If you were a small producer and were selling whiskey in barrels, it made sense to take steps to make your product as consistent as possible.
Did anyone ever routinely cycle every single barrel through some pre-determined course of rotation? Did they, for example, start all barrels high in the warehouse and then gradually move them down, like some gigantic Pachinko machine? Mike says no, but then why did they call it 'rotation,' which suggests that is exactly what they did?
One reason barrels are checked periodically is so something can be done if they are aging too fast or too slowly. What can be done is to move them from a hotter area to a cooler area or vice versa. That's barrel rotation. Maker's, for example, still does it occasionally. They have to because they only make one product and bottle in such small batches, so they need every barrel to be as much alike as possible. When you are dumping several hundred barrels for a bottling batch of Jim Beam or Jack Daniel's, that's not so important.
Does that mean Maker's moves a lot of barrels? Not necessarily. They move as many as they need to move, no more, no less. Other distilleries move barrels too, though usually it's for some other reason, such as when a warehouse is being harvested and consolidated. Barrels get removed that don't get dumped. When they are put away again, their future is taken into consideration in the selection of their new location. For all I know, that may be all Maker's is doing, but they've decided to talk about it in the context of rotation.
But, yes, it costs money every time a barrel is moved, so if you can put a barrel away once and not move it again until you dump it, that is the goal.