I think this is a good thought, but I'd rather see an indefinite number of greediness levels, instead of the four you list. Basically, just let the user set the stockpile priority to any positive integer, and haul items from lower priority stockpiles to higher priority stockpiles. For instance, a Priority 5 stockpile would take items from stockpiles with Priority 4 or lower and be used to fill stockpiles with Priority 6 or greater; a Priority 3 stockpile would fill from stockpiles with Priority 2 or 1, and be used to fill stockpiles with Priority 4 or greater. This would allow for far greater control over the hauling flow, without requiring the high-priority stockpiles to use the same greediness level.
The notion of being able to turn off hauling to stockpiles, without deleting the stockpile, is a good one; I would love to see this.
However, I'm not sure that having stockpiles filled only with clutter would serve much of a purpose. As it currently stands, clutter/mis-stockpiled items will be hauled to the nearest empty stockpile without any added actions. A clutter stockpile would fill up if there was no additional stockpile space, and empty out when there was additional stockpile space; if there was no additional stockpile space, the clutter stockpile would fill up just like a normal stockpile. As far as I can tell, this means that a stockpile that only took clutter would be precisely equivalent to a normal stockpile with the greediness feature enabled, or for that matter the existing 'take from' feature -- in either case, the stockpile would fill up when it had space and nearby workshops were cluttered, and empty out when there was additional space in a greedy and/or 'take from' stockpile.