That’s how most South Park episodes play out; they start off with an obvious and fun theme (Family Guy being an unsophisticated show), but then it evolves into some deeper and more serious theme once the satire kicks in.
Plus, while the episode pokes fun at Family Guy, there’s a scene in part 2 (or was it part I? too long ago) where after Kyle gets a ride from a man, the man tells him something. He says something like- “I really hope they don’t shut down Family Guy. Sure, it’s stupid and the jokes are shallow and stupid and have nothing to do with the plot, but sometimes I like that. At least it doesn’t get all preachy on you.”
And that was basically breaking the fourth wall in a very profound way- South Park making fun of ITSELF in an episode. I don’t think Parker and Stone were trying to say that Family Guy is an inferior show, so there’s little reason for anyone to be upset.