My understanding is that the Duggars are big Gothard followers. I don’t know if that’s true, but I have heard that.
I do know that many, many, many people have had to detox from Gothard and it is precisely the point you have made: everything in that system was about appearance (not substance) and the environment was very authoritarian. Obviously not every Gothard person had that experience. But thousands have.
And you are right: both legalism and liberalism are lies. The one is not the corrective to the other. That’s just veering out of one ditch into the other....
What you say about people who are influenced by Gothard doesn’t apply to the hundreds of Gothard people I know. It’s just in depth teaching of the Bible, it’s not a doctrine.