The most important part of your explanation involves the very last paragraph (and in particular the last sentence). Too much "science" can muddle the understanding for most humans. As one, among the many of common folk, it would make no difference to my learning if you could produce a scientist who could explain the throw in a purely scientific method--- with equations that computed the exact direction, speed and motion of the atoms comprising tori and uke. We operate in world where approximations do us the most good. And its not perfect, but works. However, I would contend that most of our understandings will continue to come from close approximations. And as teachers we need to make the most of this valued teaching tool even if its not perfect.
My response to that would be that learning poses a number of problems. Firstly, not everybody learns in the same way, probably because of different brain wiring. It remains unclear to what extent personal preference and culture are a factor in this. Nevertheless, I regularly (at university) have had students who would claim that they were visual learners, while others do not make such statements. That does not necessarily mean this is true, but of course I have no objective means for assessing this. Visual means certainly sometimes are "more fun", but something "more fun" does not mean learning is better although having that fun tend to imagine it does. Some people can learn by simply seeing teacher doing something like that whether jûdô, or dancing or drawing. Others clearly can't. Some need a lot of explanations, others don't at all.
Take music for example. Traditional music teaching stands with learning to play scales, and then finger exercises, etc. That is common, but does it have to be that way ? Why does music teaching not commonly start with playing music ? Certainly some autodidactic people have started in some very different ways, and some have reached remarkable heights.
The next issue is the depth of learning. While people learn, not everyone learns things at the same depth. Some are very superficial, others are not, some memorize, others understand. What I have always perceived in my (university) students as significant discriminator between the final outcome is the extent to which a student can do what I call diagonal learning and making connections. The really best and likely also most intelligent, can do this spontaneously, the average student seriously struggles with it. It's like comparing a standard low-budget computer with a computer build around a top processor and maximal memory; the first one may simply freeze up and not do anything anymore, the other one will do it promptly with hardly more effort than a simply calculation.
We see something in jûdô too and across the whole scale of dan-ranks. I have known high dan-ranks who have been around forever, are respected, have been in any committee, have been teachers for dozens of years, did all their time-in-grade, have won medals, yet don't know a whole lot about jûdô. I have known teachers at the Kôdôkan who when you would ask them a couple of questions about jûdô would go numb. And yet at the other end of the scale, you have people like Okano, Hirano, Daigo, who have these profound insights, skills, creativity that is totally different from others who have been in jûdô the same time.
Why ? Is this a consequence of personal limitations, or does teaching or the lack of teaching quality they've had play a significant role in this ? Why can't most people do uchi-mata ? Is it because their low motor skills, or is it because they did not have the appropriate teaching and teachers ?
These are important questions, and science does have a place in this, an important place even.
Imagine your uchi-mata sucks. Your sensei who is at least 124 years old demonstrates it and it works flawlessly, and so you ask "sense, my uchi-mata, no good, what am I doing wrong ?" So your sensei answers: "Grashopper, you are not using your ki. Use your ki and uchi-mata will follow naturally".
You are working with your friend, and your friend has perfectly learnt uchi-mata from your sensei, and you being frustrated wonder, how is that possible. So you ask you friend "Satô-san, my uchi-mata, no good, but you have learnt well from sensei. How is that ? What is your secret, how did you become so good at it?"
So, your friend answers: "afulldeck-san, before, my uchi-mata like yours, no good. But sensei told me to use my ki, so I used my ki, and now, uchi-mata good"
This scenario is not unthinkable in jûdô and from a teaching-point of view, well ... your friend Satô was able to learn it by a simply comment from your sensei, yet, you did not and in fact have no idea what is really wrong with your uchi-mata, and how on earth to have or use ki.
This is a problem, since ki does not exist as physics force. Everything that happens in martial arts is nothing more and nothing less than Newtonian mechanics.
You are in despair, but suddenly, you hear some noise, and yes, it is professor Stephen Hawking in a motorized wheelchair and dressed in jûdôgi who rides his wheel chair on to that tatami to the black board on the wall. He grabs a piece of chalk, and scribbles some mathematical formulas on the board and says: "afulldeck-san, blimey but your uchi-mata before was not very stellar. This is why".
Will your uchi-mata now be better ? Probably not. But, this example does not prove that science fails to contribute to your learning of jûdô. Both the ki-example and the Hawking-example suffer from the same problem, namely the lack of translating that material into something that is individually usable applied to your situation, and both failed to actually 'teach'. They explained, but they did not teach. Your first teacher failed to exlain what ki, is how you develop it, how you apply it and how it relates to uchi-mata, and professor Hawking failed to translate his mathematical formulas into usable practical information for you. But, Hawking was not wrong. There just was a teaching and communication problem. It is there where the skills of an accomplished teacher come in. In jûdô this problem is extremely prevalent. It is the same issue we see at the elite level, where time after time national coaches are selected because they have won themselves some Olympic, world or continental medal, something almost entirely irrelevant and useless with regard to their task. They can't teach and they are clueless about the weaknesses of their athletes and lack the insight and skills to change the process.
Of course in individual teaching it is easier to be more flexible than in group teaching where you have to create and average teaching strategy, too slow for some, too quick for others. And despite all this we should not forget that the teacher can only facilitate; at the end of the day it is still the jûdôka him-/herself who has to undergo the development and who has the responsibility to practice in order to achieve that goal. Even the best teacher will fail to optimally transfer skills to a student who does not do his/her part of the deal.