I repeat, the issue for me is the mystery that surrounds learning by ear that pretends to lead us into some better understanding of dance tunes - often played by people crammed in a small room, playing too quickly and nobody dancing antway.

There is no mystery about learning tunes by ear. You listen, you play. Simples. And, in my experience, learning this way gives you a different approach to learning a tune. I have many times seen traditional musicians pick up tunes by ear, it a quick process that centers around identifying the structure of the melody, followed by the filling in of that structure. It is completely different from approaching a tune as a string of notes, learned by heart and enables you, for one, to 'play' with the way you fill in the notes, bringing the tune to life rather than repeating it verbatim as learned each time.