I personally do not write down the music, but the idea is to learn in a way that you can write it down with some detail. I would be curious to find out if writing the notes down speeds up the process and/or improves the level of detail and accuracy of the learning. I might just try it one day when I have time.
I of course do not know if concert level performers would approve of the method since I myself am not a concert level performer
I have noticed a mixed reaction to this method with other players. I have met good piano teachers who did not even seem to understand the method. On the other hand I keep coming across people who love and understand the method well.
I personally started to do this technique in my very early 30's. I now find I can memorize more complex music faster then I could otherwise. It has completely changed the way I look at music. But this of course might just be my personal experience and/or preference.
One thing to add, the technique I described above is suitable for people with average memories like me. I am sure people with extraordinary memories and abilities to understand & hear music could take the method to whole new levels. Again I hope this is not to much info for this post! I do enjoy the topic
Also, are you encoding the music in a way that allows you to reproduce it on paper? (Ever tried writing it down?) I've had moderate success with memorizing-by-writing, but I'm only beginning to learn this stuff. I'm not actually producing facsimiles, only sketching the notes on music paper.