Rok, more and more do you display the intense listening of a true jazz aficionado; I saw that live, and not until you mentioned it just now, did I realize the weight of McCoy Tyners piano on this tune. He generates the "essence" of "My Favorite Things" as it was originally written; his piano is most certainly part of the soul of the tune; that's the part which must be captured no matter who plays it.
https://www.youtube.com/watch?v=qWG2dsXV5HITyner's piano provides the introduction, and from 2.21 to 7.05 his piano dominates the tune, after which JC takes over. That could explain why at the live performance I saw, the tune was more than 20 minutes long, because Trane went on and on; that really made the musicians happy. Kenny Rice, a professional drummer was sitting at our table, and he was in another world as Trane went on and on; mere enthusiasts such as myself were wandering (where is this train going and when is it going to stop) Somewhere else I stated exactly how long it was, that must have been much more than 20 minutes. BTW, every professional jazz musician in St. Louis was there, without their girlfriends.
Fact; me and my date were saying "enough already", it was just that long; but the musicians were ecstatic, they could have listened to this foray into the 7th galaxy all night long.
Trane had lost Tyner and Jones on his excursion into the outer limits; Tyner looked at Jones, as if to say, "We'll just hang together until the boss gets back".
Although not recorded, this was quite common at the live performances.