My Master's approach to TKD* is that the student is simply supposed to do. You follow what he says, because of his experience. What I can say is, after 6 years of training under him, I understand a lot of why he does things the way that he does. Even if a lot of things I disagree with, I come to understand his position and see how different people benefit from his way over the way I prefer. As much as I lament poomsae in this thread, and in my discussions, I've still trained them in the manner in which I've been taught - to seek to mimic closer and closer to what my Master does when he teaches me the poomsae. So if what I'm supposed to get out of it is the attention to detail and the body work, then I've accomplished that.
When I started teaching, there were a lot of things I thought he was wrong about. And also, when I started teaching, I made several kids cry and I'm pretty sure I'm the reason several more didn't make it past the 2 week trial. Since I've listened to him and done things his way, I understand more why it's that way.
Now, there are times for us to spar and experiment, but for the most part, we have to train his way. And I do (sometimes begrudgingly) and there are many, many times I look at something I've been doing for 2 years and go "oh, that's why I do that." Sometimes it's just frustrating, like having a piece of a puzzle in my hand but not knowing where it goes, because I only have the edges done so far.
*I specify this is the approach to TKD, because HKD is entirely different, and there's a lot of room to experiment and figure out what works and troubleshoot what doesn't. It's also 90% partner-based, where the TKD is maybe 25% partner-based.