It is one game, but there isn’t a truly positive case of a BB assistant winning a title or otherwise having long term NFL success. The main counter argument would of course be Nick Saban, who’s done ok in college with the same type of meticulous in game prep but also 30k foot view of the overall organization type of worldview that Bill carries. So most of the guys kinda suck, but the one guy thats most similar is unquestionably the best college coach of his era.
Not having Brady is too simple an answer - lots of coaches have not had Brady and won the Super Bowl. But I don’t think the Pats ex-coaches as HC have been less successful than non-Pats coaches as HC, so I’m just gonna say it’s a really hard job that’s success depends on faaar more than your own ability. Most people aren’t successful in the HC job. The Belichick connection and perceived success only heightens our (and others) expectations so the microscope is greater. Maybe Patricia will suck as a HC. But it’s not because he worked for NE. That’s just why he got the job in the first place.