By your measure of subpar QB play then lets include Roethlisberger 2004, Dilfer 2001, Johnson 2003, Peyton 2016. All of those teams won in spite of QB play. 4 out of 16 sounds a lot like 1/4 of the time, which sound like an exception so large that the rule needs re-examining.
But you make a great point. Why even concern ourselves with half of the game of football? Its all about having a top ten-ish QB (as measure by frequency and anecdotal timing of 3 and outs, ignoring all other statistics). Once you get yourself an Eli or a Flacco, defense is irrelevant. It was Eli's clutch throws that slowed down the game's most prolific offense and Flacco's haircut that stumped the Pats.