Rhino is being very kind about the AGA system with its somewhat less than obvious faults. What I have long attempted to do is create a balance between "looks" and "diameter versus depth". I have not tried to make the case that 1A or 1B princess cuts are ALWAYS more brilliant. I leave that up to the AGS and their scientific studies on brilliancy and light return. But, the AGA system gives the public a good grasp on a "well shaped stone" that "could" also look very good. Cutters are not fools. If they can make a stone look good with any given parameters, they will do what they can to make it happen. Ugly diamonds are really hard to sell. Some rough forces a cutter to make a deep or shallow stone. Economics and demand dictate a lot of cutting.
If one finds a very brilliant 3A or 3B princess cut, it is probably going to be overly deep and as a result the diamond, while brilliant, will have a smaller than necessary "look" for its weight....
I hope this all makes some sense to the readers here.
The AGA system strives to give the consumers the MOST bang for their bucks. Surely, we want 1A and 1B diamonds to be highly brilliant, too. That does not always occur, because rough diamonds are not all alike and cutters make decisions on how to cut every stone as best suits their own market needs.
Retailers with highly brilliant 3A or 3B diamonds may tell you how brilliant they are, but they likely know the make of the stone has something a bit or more than a bit "off". Ask specifically how the "make" is and you might get an answer. You might not.... That is why the AGA Cut grades have usefullness.