I get waht you are saying completely - that the net protein balance is determined by the average of multiple anabolic and catabolic processes. EAAs are primarily anabolic, and their ingestion maximises the anabolic response at about 0.1g per kg bodyweight. However, once the dose goes up to 0.2g per kg or beyond, plasma elevations of EAAs remain elevated more significantly and for longer (beyond the refractory rate), and become anticatabolic for around three hours - easily enough time to keep catabolism away until your next meal.
In respect of anticatabolism, if not taking any protein at all, even carbs will help here. Remember catabolism is about increasing blood glucose levels to make up for the increased oxidation occuring within the muscle, and since the body wants to spare its own glucose stores at this time, this is achieved primarily by breaking down glucogenic proteins (and recyling things like lactate and pyruvate etc but that's not relevant here) - but there are two ways around this, take in the very aminos that would otherwise be oxidised at a greater rate (EAAs) or to take carbs to provide the glucose direct.
Milk, or mixed casein and whey powders, are fine though - they defintely work enough to tip the net response into overall anabolism. From comparing various studies though using a whole range of workout supplemet protocols, my own view (which is not just my theory but pretty much based on the studies and conclusions of sports nutrition researchers like Tipton, Childs, Kravitz, Rasmussen (my fab four!)) is that EAAs are the 'most efficient' supplement or nutritional protocol, especially taken pre rather than post. There is room for growth in theory though, and it's not (to my mind) ironclad just yet - just the one that makes most sense to me.
Note I said 'most effcient' rather than 'most effective' - many other protocols are equally effective, they are just less efficient, and require higher quantities to do the same job. Also, compared to EAAs some other protocols have more potential negatives for certain people (intolerance to lactose, and beta lactoalbumin intolerance in milk products for example).
Btw, I do like casein and whey (or other combos of fast and slow proteins) combined for shakes at other times - is just around the workout where I think EAAs have the win!