Set it aside? Having grown up in that region of Texas it certainly is (wonderfully) satirical to me. It certainly isn't a hateful satire, but "too loving to be considered satire" misses it. In an otherwise very good article I'm also surprised by such a dismissal of a huge part of hit work.
Sorta like it is hard to rewatch Office Space or Idiocracy. Have to be in the right mood, every 4 or 5 years. OS was filmed in my neighborhood and until the credits rolled I thought Stephen Root (Milton) was a former coworker (physical doppelgänger) where we literally had a TPS form.
Going out for lunch with coworkers, "I hope Judge isn't sitting behind us" became a thing people would say. Freakish accuracy.
Instead, I consider KotH to be similar to the Cosby Show, Roseanne, or even All in the Family - a respectful look at the type of family that was not historically portrayed in TV or the movies.
Freudian slip of the most correct kind. It really was a hit, very odd to ignore it (fellow Texan here).