Definitely not. Most of the Kwans still exist in limited form. Mostly historically and recreationally.Well, no, the Kukkiwon was founded by the KTA after they secured quite a lot of funding from both the government and the private sector.
The South Korean government has endorsed the KTA, and as such the Kukkiwon flavor of TKD is by far the most common in South Korea, but I don't think it's illegal to teach non-Kukkiwon TKD. As I recall, the South Korean government now basically controls the Kukkiwon, but that is a relatively recent development.
I don't know what you mean by "founded by order" to be honest.