I'm not saying successful box designs haven't been built, what I'm suggesting is box designs seem a more complicated way to achieve true room integration.
I'm not sure the absolute goal is to "integrate" the speaker with the room, as much as to "recreate" the original venue's sonics in spite of the room.
Using a driver release system that must release backwave sonics that cannot do anything else but cause a reflected room distortion (sound not in the original recording) is just as problematic as the backwave being released into a cabinet.
All speakers have their trade offs and advantages. In general it will be your "preferences" as to how those trade offs are dealt with that will attract you to a design.