There is little doubt in my mind about taekkyon and ssireum - especially ssireum as the lines of transmission to Korea are so clear. Kuk Sool on the other hand is hard for me to swallow as anything other than repackaged Hapkido.
South Korean general/politician/kwan founder Choi Hong Hi formed connections with the North Korean government by giving them TKD. He eventually formed the ITF out of Canada (IIRC) after his exile from South Korea. Stronger connections with North Korea's government were formed over time. Now, after Choi's death, multiple ITFs, at least one of them controlled by North Korea, are trying to carry on.
When I first moved to Korea it really struck me as odd that no one here had any idea that there was another group of TKD. Now that I know Korea better, I am no longer surprised.
The only powerful TKD kicks are back kick, side kick, and variations of these to the head. The TKD roundhouse I always found to be relatively weak when I compared it to the Thai kick. However, the instructors and more athletic types were exceptions in my experience. I remember my old WTF TKD instructor roundhoused one of the best students in the class and he fell down clutching his chest and crawled out of the sparring area. So if you train long and hard enough you can still have a good kick in TKD. But most people just get their black belt in a year or whatever and quit.