Oh man, my biggest "promotion" was a lateral hire that I was only offered because someone owed me a solid. This is a benefit to a small group made of limited circles - when the franchise wants better odds of success, they count on people they know, or bringing in the guy who knows a guy. And when it is my turn to make a recommendation for a job, I have a rolodex to work through. Relationships count a lot when you are weeding through a sea of strangers relying on their reputation. C'est la vie mon frere. We both know it doesn't always work out - look at how the Jets gambled on Rodgers knowing who to put around him to win games, including the coaching staff!
Anyway, to the topic. I don't think we can discount that several of those top HCs also helped make the HoF QBs. Or, at the very least, some of those were "matches made in heaven" (in reference to Sean McVay, who is an excellent playcaller and never pushed a raw QB to their maximum potential - Stafford is the same QB he was in Detroit, and Goff is performing far better now than when he played for McVay). I really think that, in sum, these are all educated guesses at who can do the task - whether it is a QB or an HC, or even the damn punter. And it being an educated guess doesn't mean much, because half of the games come down to whether a kicker made a field goal or not. The Jimmys and Joes have to execute the Xs and Os, and a good program identifies how to maximize their players with good Xs and Os. Kyle Shanahan has a reputation for being that sort of coach (and is another name that my AI search missed completely - for all the excitement and fear around AI, its most remarkable trait is that it is bad at its job faster than I can ever hope to match).
I think it is more accurate to look at the other side of the coin on this one - it may be hard to find the right talent for the job, but it should be easier to rule out guys who clearly don't have it. Applied to Chicago - I think we all understand that Nagy was going to get a HC gig somewhere, and we all had reason to be excited for him to coach the Bears for a while. I think that as long as the coaching hire is someone who has shown some durable success at the NFL level, we should have some confidence that the team is heading in the right direction.
Outside of the three I named before - Vrabel, Johnson and Moore - who are your preferred candidates, and what makes you think they have "it?"