Put another way, the effort to press a key is so well within the strength constraints of any finger, it just doesn't matter.
I'm definitely with you on that point.
Where my ring finger occasionally hampers me is in situations - usually on a fretted instrument rather than a concertina - where I have to place all four fingers independently at the same time, and quick. The ring finger is sometimes slower and less accurate than the others. I usually notice this when working up a new piece, and by the time I've got the fingering into my muscle memory, the problem has gone away. Practice makes perfect!
I must point out that I've been playing the mandolin since I was about 6 years old, so at least my left ring finger never got a chance to be weak!
However, I always messed around in the sharp keys, where the pinkie is practically never used, so when I graduated to the 5-string banjo at the age of about 10, and needed 4 fingers for chords, I initially had problems with the strength and accuracy of my pinkie. By the time I took up the concertina, at 18, the weakness of the pinkie was no longer a problem.
I believe that exercise is all-important. All of us on the forum have computers with keyboards, and this is an excellent "exerciser" for musicians! Not if you type with 2 fingers, admittedly.
Make sure you use all your fingers, especially the "weak" ones!
Nevertheless, there are still those complex chords in which ring finger and pinkie, though strong and accurate enough, are noticeably less so than the index and middle fingers. The strategy I've developed here is to place the weakest, least accurate finger a split second before placing the others. In the context of plucked strings (guitar, banjo) this is possible, because the string doesn't sound until the right hand plucks it, and the right hand can wait until all the left-hand fingers are in place, irrespective of the sequence of placing them.
On the concertina, of course, a note sounds as soon as you press a button, so all notes that should sound together must be pressed together.
However, it is possible to position
the fingers one after another on the buttons, and then press them down when they're all where they should be.
Hope this helps,