I like organization but I also like to leave room for change and spontaneous planning.
I don't like to wait for something to strike me before I set off to go do it. To me spontaneous stuff doesn't make sense because everything I do must be planned, then I can control what I do, everyone works differently thats for sure. Of course now and then I might get totally distracted from what I should be studying and delve into other music. But these really distract me from my most efficient path through music. There is a lifetimes worth of music to get through, I honestly think I will die before I get through everything, but we can try!
What do you mean by "practical music"?
I mean playing piano, not theory, but yet again, theory can be sometimes very two sided but often there is a basic teacher/student relationship, unless you study composition then it's more like a shared effort, teacher trying to learn from the students ideas, the student trying to learn from the teachers superior theory.
Keep in mind, just because you didn't need to listen to what teachers told you, that doesn't mean you will have students like that!
I didn't mean to say I didn't listen to my teachers, it's just what they said made musical sense to me anyway and I would do what they say automatically because thats what I would naturally do. They simply confirmed what I thought was correct. I think this is an important way to study music, to have an idea as to how the piano should be played test these ideas, get them supported by teachers or by those listening to your playing, or by the physical feeling you get that comes from your body. Of course some beginners have 0 concept of how to play, but you force them into thinking about it no matter how feeble their ideas might seem.
I tell my students to always be comfortable, if you are comfortable then do it (some beginners might think a wrong movement is comfrotable simply because the have never experienced the most effective movement, in that case you must direct them to the better.) I ask students to always search for what is most comfortable for yourself. I really throw even my young beginner students into the deep end to question themselves, what is the best fingering and why. What the is the best way to have the hand so we don't feel tired or have difficulties while playing.
Of course I spoon feed a lot of my beginner students, set their hands in the right place by verbal directions, asking them to sense where the centre of their hands are, what the group of notes they must play are before playing them, the shape these groups produce etc etc. A lot of stuff which I learnt over years of observation of the piano I can try to train into students in a few lessons (but which too will take them years to develop). Effective ways to actually look at the piano, how to actually memorise what you play and how to read music faster, how to actually feel your fingers while they play a group of notes and how to listen to the sound you make.
Very rarely I'll actually holding their hand into place because that is too much spoon feeding imo. I try to never directly tell my students anything, just question them and push them in the right direction until they answer it themselves (sometimes this needs a lot of hints to a ridiculous point

). If they play a wrong note continuously I'll ask them something sounds wrong, I might play the passage for them with the correct note and ask them to spot the difference.
So long I am always getting them to think musically and make decisions for themselves. I think that is what I really meant by saying I am a natural musician. In the fact that I know how to invesigate music, and how to use my instruments to produce that desired sound, I knew this because I just knew how to look at music without anyone telling me, I don't know call it a gift, I think we all have musical gifts in some form, I think if you can tap a beat and rhythm you can learn music. I have a strong feeling that everyone is naturally a musician, but some must train harder than others to attain confidence that they can progress through music with their own ideas.
I like you analogy of doctor/patient, but if you are teaching begginners then that's a totally different situation, especially if they are very young.
Yeah I find this analogy even fits for beginners, there is a big disease which causes holes all over their piano technique. There is nothing there, inexperience squeezes most of the life out of their music creation. As teachers we slowly chip away at their problems, prescribing methods to promote the filling in of their technique gaps... Sounds more like a dentist filling in cavities to me now that I think about it.
For my more advanced students I find it more like an atheletics coach or something. There is not so much problems with how they play, but with how effective they are in getting to the end point of their study. You have got to increase their speed in absorbing music and now and then wipe out any bad technical habits that might creep in.