The finger rests on my concertina are hardly unnecessary, dysfunctional, mislocated or obviously designed for both the third and fourth fingers. While I can sometimes liberate the fourth finger, if I leave it free most of the time, I encounter stability and support problems, even when one end rests on my knee. In fact, it's my thumbs and pinkies that get sore when I play, not the other fingers. So I use a three-finger playing style of necessity, and play with the fourth finger only rarely (for chords that can't be covered by just three fingers).

I use the third finger to cover the pinkie-side outside row, to chord, and to facilitate legato sequences. I don't see how the way people are initially taught to play in tutorial books is at odds with the "best" way to play the instrument, unless folks get the idea they should never use the third finger or should only use certain fingers on certain rows; the books I learned from (ages ago!) never advocated such things, and I can't think of anything I had to unlearn in order to play more musically or in more complex keys. There may be some art to fingering, but it sure ain't rocket science.