Process of Head Coach interviews (merged)

I've always been curious about how the HC selection and interview process works. In my professional life, I've been on several interview panels and have been interviewed by panels, but I doubt my experience in any way reflects how it works in professional sports, particularly the NFL.

• With virtual interviews, are the candidates equipped or expected to deliver a presentation on their leadership philosophy, how they would approach 'fixing' the team, their knowledge of the roster, etc.? Or is it simply, how do you feel about this opportunity and what is your general philosophy on what it takes to be an effective head coach? I'm guessing these guys currently coaching on playoff teams don't have time to truly assess the Saints' roster? What do YOU think the questions are during virtual interviews?
  
  
• For in person interviews, does the candidate dive into their evaluation of the roster, scouting priorities, vision for the next 12-24-36 months, preferred schemes on O and D, preparation methods, motivational tactics, views on accountability, their philosophy on personnel (pure athletic traits vs. some combination of athletic traits, motor/motivation, smarts, experience at the collegiate level, etc.)? Or, is it something far different than that?
  
  
• Particularly for the Saints, would a candidate -- like Brady for example -- be ill advised to say something like:
  
  "After evaluating the roster at a high level and watching some film, I believe the injuries, while certainly an area that needs fixing with medical and training staff improvements, aren't a legitimate excuse for the subpar performance of your team. The roster needs to get younger; the team needs a new culture and identity; talent identification needs improvement; and better depth is essential. Furthermore, I don't believe Derek Carr is the answer and I would not be in favor of paying him $30 million in 2025. Frankly, Mickey, it will be a 2-3 year process of getting the roster right, drafting better, bringing on new training staff for improved conditioning and fixing the cap."
  
  I don't know ... maybe these GMs only like to hear what they want to hear and recoil from anything perceived as an attack on their performance as GM?

Anyway, it would be fascinating to know how these discussions work and how evaluations are done. Or, I'm probably overthinking it. It may be as straightforward as, "I know <insert preferred guy> and he's my choice. I'll listen to the others, but unless I'm blown away, he's who I want to move forward with."