Not sure I follow you. Yes; we all have our favorites and these may differ substantially from one person to another. As an example, in your case, you mention the particular affection you harbor for Coltrane’s "My Favorite Things". Clear enough, so far.
But you lose me here:
Which brings me to this conclusion: any music that moves you to feeling deeply is the only criterion that is fit to do justice to the incredible musicians who move us like no other and right in our listening rooms.
How does individual preference "do justice to" musicians? And what do you mean by "fit to" ? Compared to what? Which criterion would be "unfit" ? I’m not arguing semantics, here. I honestly don’t understand what you are intending to communicate.