Except that you really don't know what is generally taught or accepted.
Your assumption is incorrect Daniel. In addition to my own training, I've trained with and taught those that were very proficient in KKW TKD. You may not agree with me, but don't tell me what I know, what I've trained in or the training of those I've worked with.
The application for blocks against kicks all involve striking the side of the lower leg, which would be a deflection, not a block.
No, they don't. Not every angle of kick is going to allow you to get close to the side of the lower leg. And since your reaction is going to be slower than their action, you'll will have to take what you can get as far as a block. Claiming that you are going to be able to strike the side of the lower leg, with any degree of accuracy in a chaotic fight, with a determined attacker, as a response under duress is fallacy. You might get lucky once, depending upon the type of kick and the attackers level of skill, but it isn't something to build a sound strategy around. That is why it isn't a block or deflection movement. It is a close in strike from grappling range. Has nothing at all to do with a block/deflection of an incoming kick.
Take a look at Il Jang for an example. I've seen the down block in this form most often performed by performing the 'block/deflection' without first turning the head to the side towards the incoming threat. This means that the individual is relying upon peripheral vision to turn, execute a downward block/deflection as a reaction response to an attack that has already been launched by an attacker from the side. If the attacker is said to be attacking from the front, then you've turned your side to him while he's still in the front with a block/deflection that isn't going to take a full grown man to the side, yet the follow up is a straight punch to the side...and he isn't going to be there. A much better interpretation is you and the attacker are at grappling range, such as a clinch i.e. you've been jumped. You turn your body into him while striking with a hammer fist into his groin followed by the punch where he is going to be hunched over. It is difficult to put the movements into words and much easier to show the form and then show this interpretation live. This is not the only interpretation, I've also seen it used to demonstrate a knife hand strike and balance displacement throw. Either one demonstrates a valid principle that is a much higher % defensive movement that that of the b/p/k explanation.
This is not to say that the b/p/k interpretation for some movements are incorrect. Many are fine as presented. I prefer to look for principles of both as it provides the most meat for the student to train with. More bang for the buck. Do I expect everyone to accept my position? No, I do not. And trying to put into words what is a dynamic continuous motion isn't easy so I'll accept the blame if what I'm saying isn't coming across. I've had interpretations explained in writing to me that don't make sense but then see the demonstration and it all clicks.
With respect.