Maybe this is one of those questions that can't be answered. Like what is at Area 51 that is so secret? Who really built the pyramids? Who built Stonehenge? What is Taekwondo?
There are so many different types of Taekwondo depending on the organization and even within these organizations. Heck we have 3 schools in total and all three have a similar format for testing but our school does grappling/MMA, another only does grappling and the third does none. We are more the same then most and we are different. All Instructors trained by the same Master and trained together for more then 18 years. In fact last night my Instructor and a young black belt went over to the school I listed last as "none" to teach Kickboxing.
I don't have the answer but I also don't want to paint all Taekwondo as the same nor do I want to separate them into little categories and boxes as that would also be a nightmare in itself. Taekwondo is the umbrella with a lot of different sections underneath. This goes to what my Instructor discussed before.
A. He trained Taekwondo under his Master and when seeing other schools he could not understand why they did not do as much or were incapable of certain techniques. When he discussed this with his Master he found out that Hapkido was trained as well. When he asked why he did not show as both his Master simply answered that he was trained this way as a child. That Taekwondo was simple the umbrella that he had decided to call it.
B. Later as my Instructor trained, opened his own school and then took up other martial arts bring them back to his school and teaching; a thought did cross my Instructor. He wasn't just teaching Taekwondo but a multitude of different arts. With all of the Taekwondo bashing he actually had thought about renaming it Mixed Martial Arts but soon decided that he was proud of his Taekwondo heritage and followed in his Master's footsteps and called it Taekwondo with all the others included under the umbrella.
And if you've read any other stuff from me you may remember that I've said that most who have no experience with martial arts don't even realize that what we are being taught is not just Taekwondo. That most think this is what it is suppose to be like. It is only people like myself that got really interested in it and talked with the Instructor to find this out. We do talk about where the techniques come from but I would bet many don't pay attention as not much emphasis is put on it. They are techniques that flow together seamlessly due to good instruction by our Instructor. We never stop and say, today we are doing BJJ. Or today we are doing Hapkido. This is strictly Taekwondo. This is Muay Thai. It is Taekwondo … very simple if you don't over think it.
The thing is, you can't please everybody outside of Taekwondo as they will never understand it. For that matter you can't please everybody inside of Taekwondo as they will also never understand it. Taekwondo is many things to many people. It is an umbrella of itself or many arts blended in. It is taught the way the Instructor interprets it and wants to teach it. As long as we come together as one to announce that we love Taekwondo then that is all that really matters.