One wonders how the 4-finger technique got started in the first place. My understanding is that the CBA was an evolution of the DBA (diatonic) where one has no need to use the thumb, because with two notes on each button, your fingers do not need to move around so much. Plus, the thumb was needed to stabilize the accordion from the constant push-pull bellows action. So, the "old school" simply continued using the diatonic fingering technique on the CBA - but with very occasional thumb use on difficult passages. Also, my understanding is that the 4 row CBA was invented to make fingering easier for 4-finger playing.
I do marvel at those "old school" accordionists I see on YouTube who have such speed and dexterity using only 4 fingers. I mostly play 5-fingers, but occasionally force myself to practice 4-fingers as I find it to be good finger exercise, but then I cannot play nearly as fast. I am mostly playing a small 3-row CBA these days and can see why playing with 4-fingers is more difficult if you don't have that 4th row.
I have been burning a lot of time learning as much as I am able via the web - no direct teaching available re. CBA techniques where I live..
From what I have been able to ascertain so far, the button bisonics and the button unisonics developed at much the same time followed slightly later by the PA adaption. At much the same time, concertinas of several forms were developed.
The Soviet Union encouraged the production of 'bayan' style accordions for the education and enjoyment of the general public and their layout - three treble rows with the keyboard well forward, away from the player's body - created a style of playing with the thumb behind the keyboard which, unless unless the 'pinky' was unusually long, meant that only three fingers of the treble hand were generally usable.
In Europe a whole range of significantly different forms of squeezeboxes were in development and, when they arrived in the Americas were adapted to suit local requiremments.
The domination by the PA in North America was a result of a form of social snobbery where buttons were considered low class and the clavier more 'educated'; hence the 'finto' keyboard made for Pietro Frosini who, despite being educated at the Milan Conservatory, needed to present an appearance of piano-style keys on his CBAs in order to be accepted by the paying public. Generally the 'piano' keyboard adoption was also more common where initial music training was conducted on actual pianos, or by direct reference to them in theory teaching, with most people not understanding the advantages of the CBA layout and/or being reluctant to spend the effort needed to adapt.
The modern CBA keyboard is positioned similarly to that of the PA and some versions have six rows of keys with which to facilitate the rapid fingering required for 'Balkan' style music.
The great advantage of the CBA layout is its flexibility in 'fingering' which can be adapted for each piece and/or phrase in music as found most suitable to the individual performer.
Watch
https://www.youtube.com/@Hrustevich closely on any of his classical pieces to see how he has no 'hard-and-fast' playing forms and
https://www.youtube.com/@AlfHagedal effortlessly making all kinds of music on a three row CBA ( some of them 'finto') with Richard Galliano
https://www.youtube.com/@richardgalliano3487/videos bending every 'rule' that there is to bend (as well as a few notes, too).
Magic stuff all over the bellows driven 'free reed' world