Piotr's setup is for recording. It's not trivial to use the same setup for amplification but with very careful placement of mics versus speakers it can be done. For recording it's always best to use microphones at some distance of the accordion, left and right, to get the most natural sound pickup. For amplification you want something inside or very close to the accordion to reduce the risk of feedback loops.
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I suspect that mics placed a couple of feet away would also pick up less button (and other mechanical) noise, particularly on bandoneons.
On a bandoneon, maybe, I don't know. But on an accordion I do have experience making recordings with mics placed a couple of feet away and they do pick up button and other mechanical noise "quite well". When you have mics under the grille they do not pick up keyboard noise as much, but they do still pick up a bit of noise from key release (pallets closing). The only way to reduce mechanical noise (like key clacks) is to just play louder.
Indeed, but not just louder, but also avoiding going too loud. If you were to use the full dynamic range of a good accordion then the recording would show clipping in very loud parts. If you adjust the volume to avoid clipping then parts played in pp would drown in not just mechanical noise but also electronic noise.
Yes the gooseneck microphones are good and flexible however they don't give great coverage over the entire treble keyboard and they cables can be difficult to manage. With internal mikes you have better cable management and have volume control at your fingertips.
