I will preface with two things: first and foremost, my compliments to the entire staff and particularly to you for your interesting videos that are accessible to everyone; and secondly, I am aware of the two schools of thought (fingers vs. weight) and I am much, much more oriented towards the latter.
My opinion differs from yours essentially on the initial part, while agreeing on the final result: playing relaxed by exploiting every "trick," inter-intra-dependence of weight, anticipating the thought, playing directly on the strings etc. etc.—only in this way can one, at least in potential, sing.
My experience is rare; as already mentioned, I have continued to play modern music and liscio accordion (so I only play with the right hand) for at least twenty years. Besides octave bass notes to follow the chords, the left hand has never done anything else, while the right hand has become bastardized over these years, since the faster you go, the better you are, and it doesn't matter if out of 100 notes, 30 are pieces [muddled], not to mention the lack of phrasing...
Since July, in addition to playing Bach for two hours a day, I listen extensively to professional pianists, comparing their interpretations. No Hanon, scales, or arpeggios. Only the Inventions. And studying them by memory from the very beginning, because if I start by studying them by reading, I am no longer able to visualize the score later while NOT playing them.
Obviously, hands separate until the speed and fluency are slightly above the final speed.
As soon as I notice that a passage isn't working, I cycle and cycle and then cycle again. No rhythm variations, and on this, I agree with thesimon.
When joining the hands, I don't need to look at the right hand. The right hand is bastardized but has achieved full awareness of the keys. It is a sensation that is difficult to explain, but in practice, even after a leap, it goes to the right note without looking and, above all, has a secure grip on every key.
The work I am doing on the right hand is comparable to teaching classical dance to someone who knows how to dance hip-hop well. Refining. And this happens on two levels: physical and, above all, mental (and here the listening to the masters helps).
I also take advantage of Chan when he says that one hand can teach the other through imitation.
Once the left hand has reached the right degree of awareness of the keyboard, I join them.
And I start studying by memory with hands together, dividing and joining various blocks of code.
When I feel confident, I refine the phrasing by exaggerating.
At the end of all this rambling, I record myself. And this first recording serves only to "hype myself up" and relieve performance anxiety.
Now I can enjoy singing the piece and not think about the fingers, the notes, etc. etc.; I am relaxed, and mentally my whole body must ensure that what I sing materializes instantaneously on the instrument.