The division of the merits of buddy (B) vs. solo (S) diving into the categories of a system (SYS) and its implementation (IMP) is interesting. I'd like to analyze some of the arguments within the framework of these categories. We need to level the playing field. To eliminate all the IMP level problems with B diving we'll assume you and your buddy are equal and do all the required things needed to implement a fully functional buddy team. Looking at the dive styles from a system POV I hope to eliminate some of the emotional bias that distorts an objective viewpoint. Most of what I present here is not new; Others in this thread have already said it.
From S diving POV:
Let's take the issue of an alternate air supply. Some have argued that this is an advantage for S diving over B. To level the playing field let's give each diver in the B pair their own alternate air souces. [You may object, saying this isn't done in the real world. But, were evaluating based on the system and not on what actually happens which is IMP.] What appears to be an advantage in S disappears.
Solitude. Another advantage in S diving. Can we add solitude to B diving. No, by definition B diving requires communication between the B pair. Solitude remains an advantage.
Less bandwidth [SIC] equals less effort over B diving therefore an advantage. So we're on the same page [mental] bandwidth is the amount and effort of thinking about your buddy which includes but is not limited to communication, position, welfare, etc. Obviously, it remains an advantage but a trivial one. Think of all the small tasks you do every day from the time you wake up in the morning to the time you arrive at work (get out of bed, walk to the bathroom, go to the bathroom, brush your teeth, wash your face, get dressed, eat breakfast, etc. I haven't even got to driving to work yet.) This is a at least a 1000 times more than what you do with your buddy underwater. If you can't manage the relatively few underwater tasks, how in the world do you get through your day?
From B diving POV:
Additional awareness. An advantage for B diving? Can we add someone to S. No, based on the definition of S diving. B diving retains advantage.
Additional brain. An advantage for B diving? Same as above.
Additional hands. An advantage for B diving? Same as above.
All the problems associated with the B system can be corrected by correct implementation. For example, a common complaint is your buddy swims away leaving you alone. This is solved by reinstructing your buddy or getting a new buddy. The same approach can be used to solve virtually all the buddy problems.
Where does this leave us? As a system buddy diving is clearly superior and this is why virtually every source I've read favors B diving over S diving. The dive plan sometimes dictates the choice of dive system. Photographers might prefer S over B. Cave divers will prefer B over S.