It's a very easy, "universal" system that you use as a base for playing everything, and it keeps your hand in comfortable & relaxed position. C row & D row fingering are reasonably similar (unlike the 3-row keyboard where the 3 row fingerings are wildly different), and you only alter your fingerings if there's a good reason for it (you'll figure it out yourself, as everything is very intuitive).
Tcabot's description of the B-system fingering he is using is a revelation to me. Now I finally understand some of the comments that the C system makes no logical sense, or that 3-row systems require wildly different fingering. When talking about preferences for CBA keyboards, it is not just the button layout, but also the number of rows and fingering patterns across the rows that are important to understanding these preferences. Unlike the PA, there are a number of different ways to play a CBA.
Both of my CBA boxes are of French design, and as the traditional French school promotes playing primarily on 3 rows (on a C system), one of my instruments is 4 row and the other a very compact 3 row, no bigger than a melodeon. I never thought much about playing as tcabot prefers across all five rows (if I had a five row). So, on a three row, there are three fingering patterns one must learn (and I never considered them to be wildly different). The only reason for choosing a five-row instrument, by my previous understanding, is that you can then play in any key using any of the three three-row fingering patterns.
I will point out that tcabot's B-system fingering across all five rows would work equally well with a five-row C system, only the up and down diagonals would be reversed.
As for the traditional French school of playing, by my understanding, it is even more restrictive than playing primarily on three rows. They also teach you to rarely use your thumb or pinky finger, but mostly only the first three fingers unless you encounter a very awkward phrase. In this case, you are allowed to reach up to the helper row (if you have the fourth row) or even use your thumb. At least this is my understanding from what I have read and observed on videos. (I am self-taught, and only learned about this later on.) If someone knows differently, please correct my description!
To someone who likes to play across all five rows, this must seem almost crazy restrictive. Yet, there are many incredibly good French musicians who play this way. We humans can adapt to almost anything with enough practice. As for myself, I have tried the French way of playing, but I tend to use all five fingers across the three rows most of the time.
Here is one example of this type of playing. Although Sebastien is playing a five-row here, if you observe closely, you will see that he rarely uses anything other than the first three fingers and the first three rows.