Focused approach helps the teacher to deliver what's required - I don't believe it's of any help to the learner/player.
Then there is the problem of increased speed - i.e. if I want to do a quick scale but with a certain nuance, I play each individual note at a certain volume - yet it becomes increasingly difficult for me to retain this clarity and volume as my speed increases.
I agree with you 100% - for you.I don't learn that way. I need the other approach.
There are two standard approaches.One is the goal focused method, suggested by hardy. Have a clear and powerful image of the sound you want, and don't worry too much about exactly how you get it. This is sometimes called Inner Tennis after the book by Gallwey. The other is the method focused approach. Learn what it is you do differently when it works. Is it a forearm relaxation, a shoulder rotation, a careful curvature of the finger, etc.? Once you know how it's done, you know how to reproduce it, and you can analyze why when it goes wrong.
For example, staccato was a sharp poke with pokey-fingers that were stiff and ineffective for anything faster.
I'll go with experimenting, and I won't preclude starting with physical motions and hearing what happens, in that experimentation. In regards to having inner feelings lead the way, that is what I did most of my life because I had to do music on my own. I would often produce the sound that I heard in my head but they were not necessarily the ideal way of going about it.
Staccato is often a 'sharp poke with pokey-fingers' (when it's loud for instance). The secret is having 'pokey-fingers' for only milliseconds (1000'ths of a second).