May I add something to it:
Does this always implies being able to play from memory ?
And if yes, to what extent is Harmony a principle key to achieve this goal ?
I didn't follow any music school, if you read my story. So I'm missing the whole theory cycle, although I am quite good in sight reading.
My story also contains the fact that my heath is not so good.
I would like to put energy, of which I don't have much, in theory and harmony, in order to progress in the domain of analysis of pieces, being able to play by memory...
Otherwise I feel quite comfortable as it is.
Only, once the romantics come around the corner, harmonies are complexer, lot of chords, triads, and so on. I think these things should be trained upfront, by ear training, theory and harmony.