I agree that the story may only be used as a illustration and may, or may not be, based on an actual event. However, it is a nice story
So let us consider something that is known, or at least has been passed on;
1) Yip Man is said to have practiced the SNT slowly and is reported to have taken a good deal of time to perform it. I believe I heard somewhere that it could sometimes take up to 45 minutes. Of course, my info is second hand as I was not there. However, if true, it would indicate that he saw value in training the form slowly. Perhaps not every day but on some instances.
2) In Japanese arts you have "Do" arts which were the more refined or "sport" versions of their sister arts. Judo and Kendo for example. In the "Do" arts there is a "spiritual" element as well. What I am getting at is that an art like Judo is designed for self development as well as learning the art. Also, for Judo to work you must be able to connect with your opponent. In essence your throw will only work if you are in concert with the opponent. For example, to apply a throw when your opponent steps forward you must apply the correct amount of force, too much or too little and your throw will potentially fail. This implies a need for great sensitivity to the energy provided. Of course there are many factors involved in a good throw but disrupting balance is the keystone and to disrupt the balance one must be aware of the opponent and work with what they give you.
3) Many of the past masters recommended studying other things in order to achieve balance in life. Some, as you suggest, started such study after already assuring their reputation. However, many also felt that it was important to achieve such a balance not only for the art they trained but for life itself.
I have always been blessed with an attitude of "I don't care" so the idea of "Mushin" has always been of interest to me. Not claiming to have achieved this state, but will say it intrigues me and I would think that to attain it one would need something other than "fast" practice.
Of course, meditation is like anything else..............it is not the end all or goal...............just another piece of the pie.
Still, how many times have we heard sayings like; "it is not the size of the dog in the fight, but the size of the fight in the dog"? Seems to me that there is an accepted agreement that combat requires a mental component. The question would seem to be how one develops that mental component. I would propose that meditation, slow training are one way of development. Then again, getting hit and learning to take punishment is another way. I will not speculate on which one is more effective or produces results faster.